CINXE.COM

<!DOCTYPE html> <html class="client-nojs" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Category:Geometric group theory - Wikimedia Commons</title> <script>(function(){var className="client-js";var cookie=document.cookie.match(/(?:^|; )commonswikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy","wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"c97ba40c-5da2-4c14-a5b5-a8f8208e502b","wgCanonicalNamespace":"Category","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":14,"wgPageName":"Category:Geometric_group_theory","wgTitle":"Geometric group theory","wgCurRevisionId":308659594,"wgRevisionId":308659594,"wgArticleId":49059,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null, "wgUserGroups":["*"],"wgCategories":["Uses of Wikidata Infobox","Uses of Wikidata Infobox with no image","Geometry","Group theory"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Category:Geometric_group_theory","wgRelevantArticleId":49059,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"commons","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":false,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":200,"wgCentralAuthMobileDomain":false,"upwizPropertyTitles":{"P180":"Main subjects visible in this work"},"upwizPropertyPlaceholders":{"P180":"e.g., Angolan giraffe"},"upwizPropertyCopyLabels":{ "P180":"Main subjects"},"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"personal","wgULSisCompactLinksEnabled":true,"wgVector2022LanguageInHeader":false,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q8488080","wbmiDefaultProperties":["P180"],"wbmiPropertyTitles":{"P180":"Items portrayed in this file"},"wbmiPropertyTypes":{"P180":"wikibase-item"},"wbmiRepoApiUrl":"/w/api.php","wbmiHelpUrls":{"P180":"https://commons.wikimedia.org/wiki/Special:MyLanguage/Commons:Depicts"},"wbmiExternalEntitySearchBaseUri":"https://www.wikidata.org/w/api.php","wbmiSupportedDataTypes":["wikibase-item","string","quantity","time","monolingualtext","external-id","globe-coordinate","url"],"wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"]};RLSTATE={"ext.gadget.Long-Image-Names-in-Categories":"ready","ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user": "ready","user":"ready","user.options":"loading","mediawiki.action.styles":"ready","ext.categoryTree.styles":"ready","mediawiki.page.gallery.styles":"ready","mediawiki.helplink":"ready","skins.vector.styles.legacy":"ready","jquery.makeCollapsible.styles":"ready","ext.tmh.player.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","codex-search-styles":"ready","ext.uls.pt":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["mmv.bootstrap","ext.categoryTree","site","mediawiki.page.ready","jquery.makeCollapsible","skins.vector.legacy.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.Slideshow","ext.gadget.ZoomViewer","ext.gadget.CollapsibleTemplates","ext.gadget.fastcci","ext.gadget.Stockphoto","ext.gadget.WatchlistNotice","ext.gadget.AjaxQuickDelete","ext.gadget.WikiMiniAtlas","ext.gadget.LanguageSelect","ext.gadget.PictureOfTheYearEnhancements","ext.tmh.player","ext.urlShortener.toolbar", "ext.centralauth.centralautologin","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.wikimediaEvents.wikibase","ext.navigationTiming","ext.uls.compactlinks","ext.uls.interface","ext.checkUser.clientHints","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=codex-search-styles%7Cext.categoryTree.styles%7Cext.tmh.player.styles%7Cext.uls.pt%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cjquery.makeCollapsible.styles%7Cmediawiki.action.styles%7Cmediawiki.helplink%7Cmediawiki.page.gallery.styles%7Cskins.vector.styles.legacy%7Cwikibase.client.init&only=styles&skin=vector"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.gadget.Long-Image-Names-in-Categories&only=styles&skin=vector"> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector"> <meta name="generator" content="MediaWiki 1.44.0-wmf.5"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Category:Geometric group theory - Wikimedia Commons"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//commons.m.wikimedia.org/wiki/Category:Geometric_group_theory"> <link rel="alternate" type="application/x-wiki" title="Edit" href="/w/index.php?title=Category:Geometric_group_theory&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/commons.png"> <link rel="icon" href="/static/favicon/commons.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikimedia Commons"> <link rel="EditURI" type="application/rsd+xml" href="//commons.wikimedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://commons.wikimedia.org/wiki/Category:Geometric_group_theory"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/"> <link rel="alternate" type="application/atom+xml" title="Wikimedia Commons Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin-vector-legacy mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-14 ns-subject mw-editable page-Category_Geometric_group_theory rootpage-Category_Geometric_group_theory skin-vector action-view"><div id="mw-page-base" class="noprint"></div> <div id="mw-head-base" class="noprint"></div> <div id="content" class="mw-body" role="main"> <a id="top"></a> <div id="siteNotice"></div> <div class="mw-indicators"> <div id="mw-indicator-mw-helplink" class="mw-indicator"><a href="/wiki/Commons:Categories" target="_blank" class="mw-helplink"><span class="mw-helplink-icon"></span>Help</a></div> </div> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-namespace">Category</span><span class="mw-page-title-separator">:</span><span class="mw-page-title-main">Geometric group theory</span></h1> <div id="bodyContent" class="vector-body"> <div id="siteSub" class="noprint">From Wikimedia Commons, the free media repository</div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="contentSub2"></div> <div id="jump-to-nav"></div> <a class="mw-jump-link" href="#mw-head">Jump to navigation</a> <a class="mw-jump-link" href="#searchInput">Jump to search</a> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r905765184">.mw-parser-output #wdinfobox[dir="ltr"]{float:right;clear:right;margin-right:0;margin-left:1em}.mw-parser-output #wdinfobox[dir="rtl"]{float:left;clear:left;margin-left:0;margin-right:1em}.mw-parser-output #wdinfobox{width:258px;box-sizing:border-box;font-size:95%;padding:0}.mw-parser-output #wdinfobox .image img{max-width:250px;max-height:250px;width:auto}.mw-parser-output #wdinfoboxcaption{background:#FFF}.mw-parser-output #wdinfobox[dir="ltr"] #wdinfoboxcaption{margin-left:0}.mw-parser-output #wdinfobox[dir="rtl"] #wdinfoboxcaption{margin-right:0}.mw-parser-output #wdinfobox th,.mw-parser-output #wdinfo_taxon th{vertical-align:top;word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox td,.mw-parser-output #wdinfo_taxon td{word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox li:not(:last-child){margin-bottom:3px}.mw-parser-output #wdinfo_taxon{font-size:95%;table-layout:fixed;padding:0}.mw-parser-output .taxontree-lcell,.mw-parser-output .wikidatainfobox-lcell{background:#CFE3FF;padding-left:.4em;padding-right:.4em;font-weight:bold}.mw-parser-output .taxontree-rcell,.mw-parser-output .wikidatainfobox-rcell{word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox[dir="ltr"] .taxontree-lcell,.mw-parser-output #wdinfobox[dir="ltr"] .wikidatainfobox-lcell{text-align:right;word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox[dir="rtl"] .taxontree-lcell,.mw-parser-output #wdinfobox[dir="rtl"] .wikidatainfobox-lcell{text-align:left;word-wrap:break-word;hyphens:auto}.mw-parser-output .taxontree-fullcell{text-align:center}.mw-parser-output .taxontree-hdrcell{text-align:center;background:#CFE3FF;padding-left:.4em;padding-right:.4em;font-weight:bold}.mw-parser-output .taxontree-row{}@media screen and (max-width:600px){.mw-parser-output .wdinfo_nomobile{display:none;visibility:hidden;height:0}}.mw-parser-output .wdinfobox_horizontal{clear:both!important;display:block;box-sizing:border-box!important;width:100%!important;column-width:24em}.mw-parser-output .wdinfobox_hide{display:none}.mw-parser-output #wdcreator{display:none}.mw-parser-output .wdcreator_show{display:block!important}.mw-parser-output #wdinfo_taxon ul{list-style:none;list-style-position:inside}.mw-parser-output #wdinfobox[dir="ltr"] #wdinfo_taxon ul{padding-left:0;margin-left:0}.mw-parser-output #wdinfobox[dir="rtl"] #wdinfo_taxon ul{padding-right:0;margin-right:0}.mw-parser-output .wikidatainfoboxVN ul li{list-style:none;padding:0;margin:0}.mw-parser-output .wikidatainfoboxVN ul{margin-left:0}.mw-parser-output .wikidatainfoboxVN{padding:0;margin:0}</style><div style="display:none"><nowiki>teoría geométrica de grupos; 幾何羣論; théorie géométrique des groupes; Геометрическая теория групп; Geometrische Gruppentheorie; Lý thuyết nhóm hình học; 幾何群論; teoria geometrică a grupurilor; 幾何学的群論; geometria grupa teorio; геометрична теорія груп; meetkundige groepentheorie; 幾何群論; Γεωμετρική θεωρία ομάδων; 几何群论; geometriai csoportelmélet; geometric group theory; نظرية الزمر الهندسية; geometrická teorie grup; teoria geométrica de grupos; área de las matemáticas que se dedica al estudio de los grupos finitamente generados; розділ математики; area in mathematics devoted to the study of finitely generated groups; Teoria geométrica de grupo; Teoria geometrica de grupos; Teoría geométrica de grupo; Teoría geometrica de grupo; Teoría geometrica de grupos; Teoria geométrica de grupos; Teoria geometrica de grupo; グロモフの理論; geometrikus csoportelmélet; 几何群论; 幾何羣論</nowiki></div><table id="wdinfobox" dir="ltr" class="fileinfotpl-type-information vevent infobox mw-collapsible"><caption class="fn org" id="wdinfoboxcaption"><b>geometric group theory </b></caption><tbody><tr><td colspan="2" class="wdinfo_nomobile" style="text-align:center"><div>area in mathematics devoted to the study of finitely generated groups</div><div class="switcher-container"></div></td></tr><tr><td colspan="2" style="text-align:center"><b><a class="external text" href="https://commons.wikimedia.org/w/index.php?title=Special%3AUploadWizard&categories=Geometric+group+theory">Upload media</a></b></td></tr><tr><td colspan="2" style="text-align:center; font-weight:bold"><div><span typeof="mw:File"><span><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/16px-Wikipedia-logo-v2.svg.png" decoding="async" width="16" height="15" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/24px-Wikipedia-logo-v2.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/32px-Wikipedia-logo-v2.svg.png 2x" data-file-width="103" data-file-height="94" /></span></span> <a href="https://en.wikipedia.org/wiki/Geometric_group_theory" class="extiw" title="en:Geometric group theory">Wikipedia</a></div></td></tr><tr class="wdinfo_nomobile"><th class="wikidatainfobox-lcell">Subclass of</th><td><div class="plainlist"><ul><li><a href="/wiki/Category:Group_theory" title="Category:Group theory">group theory</a></li></ul></div></td></tr><tr><td colspan="2"><table style="width:100%" id="wdinfo_ac" class="mw-collapsible"><tbody><tr><th style="background: #cfe3ff">Authority file</th></tr><tr><td style="text-align: center;"><div style="overflow-wrap: break-word; font-size: smaller"><span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q2662474" title="d:Q2662474"><img alt="Wikidata" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> <a href="https://www.wikidata.org/wiki/Q2662474" class="extiw" title="d:Q2662474">Q2662474</a><br /><span class="wdinfo_nomobile">NL CR AUT ID: <span><span><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph1050831">ph1050831</a></span></span></span></div></td></tr><tr class="wdinfo_nomobile"><td colspan="2" style="text-align: center"><small><div class="hlist hlist-separated"><ul><li><span style="white-space:nowrap"><a class="external text" href="https://reasonator.toolforge.org/?q=Q2662474">Reasonator</a></span></li><li><span style="white-space:nowrap"><a href="https://iw.toolforge.org/scholia/Q2662474" class="extiw" title="toolforge:scholia/Q2662474">Scholia</a></span></li><li><span style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://wikidocumentaries-demo.wmcloud.org/Q2662474">Wikidocumentaries</a></span></li><li><span style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://petscan.wmflabs.org/?language=commons&categories=Geometric_group_theory&project=wikimedia&ns%5B6%5D=1">PetScan</a></span></li><li><span style="white-space:nowrap"><a class="external text" href="https://glamtools.toolforge.org/glamorgan.html?&category=Geometric_group_theory&depth=1&month=last">statistics</a></span></li><li><span style="white-space:nowrap"><a class="external text" href="https://wikimap.toolforge.org/?cat=Geometric_group_theory&subcats=true&subcatdepth=1&cluster=true">WikiMap</a></span></li><li><span style="white-space:nowrap"><a class="external text" href="https://locator-tool.toolforge.org/#/geolocate?category=Geometric_group_theory">Locator tool</a></span></li><li><span style="white-space:nowrap"><a class="external text" href="https://kmlexport.toolforge.org/?project=commons&article=Category%3AGeometric+group+theory">KML file</a></span></li><li><a href="/wiki/Special:Search/haswbstatement:P180%3DQ2662474" title="Special:Search/haswbstatement:P180=Q2662474">Search depicted</a></li></ul></div></small></td></tr></tbody></table></td></tr><tr class="wdinfo_nomobile"><td lang="en" colspan="2" style="text-align:right"><span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q2662474" title="Edit infobox data on Wikidata"><img alt="Edit infobox data on Wikidata" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/23px-Blue_pencil.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/30px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></td></tr></tbody></table> <p>Images relating to the mathematical field of <a href="https://en.wikipedia.org/wiki/geometric_group_theory" class="extiw" title="en:geometric group theory">geometric group theory</a>. </p>    </div><div class="mw-category-generated" lang="en" dir="ltr"><div id="mw-subcategories"> <h2>Subcategories</h2> <p>This category has the following 2 subcategories, out of 2 total. </p><div lang="en" dir="ltr" class="mw-content-ltr"><div class="mw-category"><div class="mw-category-group"><h3>B</h3> <ul><li><div class="CategoryTreeSection"><div class="CategoryTreeItem"><span class="CategoryTreeEmptyBullet"></span> <bdi dir="ltr"><a href="/wiki/Category:Buekenhout_geometry" title="Category:Buekenhout geometry">Buekenhout geometry</a></bdi> <span title="Contains 0 subcategories, 0 pages, and 3 files" dir="ltr">(3 F)</span></div><div class="CategoryTreeChildren" style="display:none"></div></div></li></ul></div><div class="mw-category-group"><h3>D</h3> <ul><li><div class="CategoryTreeSection"><div class="CategoryTreeItem"><span class="CategoryTreeBullet"><a class="CategoryTreeToggle" data-ct-title="Discrete_groups" aria-expanded="false"></a> </span> <bdi dir="ltr"><a href="/wiki/Category:Discrete_groups" title="Category:Discrete groups">Discrete groups</a></bdi> <span title="Contains 2 subcategories, 0 pages, and 0 files" dir="ltr">(2 C)</span></div><div class="CategoryTreeChildren" style="display:none"></div></div></li></ul></div></div></div> </div><div id="mw-category-media"> <h2>Media in category "Geometric group theory"</h2> <p>The following 19 files are in this category, out of 19 total. </p><ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Abelian.svg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Abelian.svg/90px-Abelian.svg.png" decoding="async" loading="lazy" width="90" height="120" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Abelian.svg/134px-Abelian.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Abelian.svg/179px-Abelian.svg.png 2x" data-file-width="293" data-file-height="392" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Abelian.svg" class="galleryfilename galleryfilename-truncate" title="File:Abelian.svg">Abelian.svg</a> 293 × 392; 63 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/120px-Automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" decoding="async" loading="lazy" width="120" height="51" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/180px-Automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/240px-Automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg 2x" data-file-width="977" data-file-height="412" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" class="galleryfilename galleryfilename-truncate" title="File:Automate de l'allumeur de réverbères.jpg">Automate de l'allumeur de réverbères.jpg</a> 977 × 412; 61 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Automate_de_Mealy_du_groupe_de_Grigorchuk.jpg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/60/Automate_de_Mealy_du_groupe_de_Grigorchuk.jpg/120px-Automate_de_Mealy_du_groupe_de_Grigorchuk.jpg" decoding="async" loading="lazy" width="120" height="102" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/6/60/Automate_de_Mealy_du_groupe_de_Grigorchuk.jpg/180px-Automate_de_Mealy_du_groupe_de_Grigorchuk.jpg 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/6/60/Automate_de_Mealy_du_groupe_de_Grigorchuk.jpg/240px-Automate_de_Mealy_du_groupe_de_Grigorchuk.jpg 2x" data-file-width="645" data-file-height="550" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Automate_de_Mealy_du_groupe_de_Grigorchuk.jpg" class="galleryfilename galleryfilename-truncate" title="File:Automate de Mealy du groupe de Grigorchuk.jpg">Automate de Mealy du groupe de Grigorchuk.jpg</a> 645 × 550; 41 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Automate_de_Sushchanskii.jpg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Automate_de_Sushchanskii.jpg/120px-Automate_de_Sushchanskii.jpg" decoding="async" loading="lazy" width="120" height="96" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Automate_de_Sushchanskii.jpg/180px-Automate_de_Sushchanskii.jpg 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Automate_de_Sushchanskii.jpg/240px-Automate_de_Sushchanskii.jpg 2x" data-file-width="669" data-file-height="537" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Automate_de_Sushchanskii.jpg" class="galleryfilename galleryfilename-truncate" title="File:Automate de Sushchanskii.jpg">Automate de Sushchanskii.jpg</a> 669 × 537; 60 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Cancelling.gif" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Cancelling.gif/95px-Cancelling.gif" decoding="async" loading="lazy" width="95" height="120" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Cancelling.gif/142px-Cancelling.gif 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Cancelling.gif/189px-Cancelling.gif 2x" data-file-width="477" data-file-height="604" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Cancelling.gif" class="galleryfilename galleryfilename-truncate" title="File:Cancelling.gif">Cancelling.gif</a> 477 × 604; 12.95 MB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Candidates.jpg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Candidates.jpg/120px-Candidates.jpg" decoding="async" loading="lazy" width="120" height="16" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Candidates.jpg/180px-Candidates.jpg 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Candidates.jpg/240px-Candidates.jpg 2x" data-file-width="819" data-file-height="111" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Candidates.jpg" class="galleryfilename galleryfilename-truncate" title="File:Candidates.jpg">Candidates.jpg</a> 819 × 111; 13 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Delta_thin_triangle_condition.svg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Delta_thin_triangle_condition.svg/120px-Delta_thin_triangle_condition.svg.png" decoding="async" loading="lazy" width="120" height="88" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Delta_thin_triangle_condition.svg/180px-Delta_thin_triangle_condition.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Delta_thin_triangle_condition.svg/240px-Delta_thin_triangle_condition.svg.png 2x" data-file-width="321" data-file-height="235" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Delta_thin_triangle_condition.svg" class="galleryfilename galleryfilename-truncate" title="File:Delta thin triangle condition.svg">Delta thin triangle condition.svg</a> 321 × 235; 6 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Dual_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Dual_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/120px-Dual_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" decoding="async" loading="lazy" width="120" height="51" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Dual_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/180px-Dual_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Dual_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/240px-Dual_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg 2x" data-file-width="981" data-file-height="416" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Dual_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" class="galleryfilename galleryfilename-truncate" title="File:Dual de l'automate de l'allumeur de réverbères.jpg">Dual de l'automate de l'allumeur de réverbères.jpg</a> 981 × 416; 36 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Grigorchuk_group_generators.svg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Grigorchuk_group_generators.svg/120px-Grigorchuk_group_generators.svg.png" decoding="async" loading="lazy" width="120" height="52" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Grigorchuk_group_generators.svg/180px-Grigorchuk_group_generators.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Grigorchuk_group_generators.svg/240px-Grigorchuk_group_generators.svg.png 2x" data-file-width="2789" data-file-height="1216" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Grigorchuk_group_generators.svg" class="galleryfilename galleryfilename-truncate" title="File:Grigorchuk group generators.svg">Grigorchuk group generators.svg</a> 2,789 × 1,216; 118 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:HeisenbergCayleyGraph.png" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c7/HeisenbergCayleyGraph.png/120px-HeisenbergCayleyGraph.png" decoding="async" loading="lazy" width="120" height="95" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c7/HeisenbergCayleyGraph.png/180px-HeisenbergCayleyGraph.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/c/c7/HeisenbergCayleyGraph.png/240px-HeisenbergCayleyGraph.png 2x" data-file-width="533" data-file-height="423" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:HeisenbergCayleyGraph.png" class="galleryfilename galleryfilename-truncate" title="File:HeisenbergCayleyGraph.png">HeisenbergCayleyGraph.png</a> 533 × 423; 9 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Inverse_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Inverse_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/120px-Inverse_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" decoding="async" loading="lazy" width="120" height="51" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Inverse_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/180px-Inverse_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Inverse_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/240px-Inverse_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg 2x" data-file-width="979" data-file-height="413" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Inverse_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" class="galleryfilename galleryfilename-truncate" title="File:Inverse de l'automate de l'allumeur de réverbères.jpg">Inverse de l'automate de l'allumeur de réverbères.jpg</a> 979 × 413; 66 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Paradoxical_decomposition_F2.png" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Paradoxical_decomposition_F2.png/120px-Paradoxical_decomposition_F2.png" decoding="async" loading="lazy" width="120" height="115" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Paradoxical_decomposition_F2.png/180px-Paradoxical_decomposition_F2.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Paradoxical_decomposition_F2.png/240px-Paradoxical_decomposition_F2.png 2x" data-file-width="2977" data-file-height="2864" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Paradoxical_decomposition_F2.png" class="galleryfilename galleryfilename-truncate" title="File:Paradoxical decomposition F2.png">Paradoxical decomposition F2.png</a> 2,977 × 2,864; 104 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Paradoxical_decomposition_F2.svg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/09/Paradoxical_decomposition_F2.svg/120px-Paradoxical_decomposition_F2.svg.png" decoding="async" loading="lazy" width="120" height="115" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/0/09/Paradoxical_decomposition_F2.svg/180px-Paradoxical_decomposition_F2.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/0/09/Paradoxical_decomposition_F2.svg/240px-Paradoxical_decomposition_F2.svg.png 2x" data-file-width="359" data-file-height="344" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Paradoxical_decomposition_F2.svg" class="galleryfilename galleryfilename-truncate" title="File:Paradoxical decomposition F2.svg">Paradoxical decomposition F2.svg</a> 359 × 344; 193 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Pentagon_reflection_composition.png" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/48/Pentagon_reflection_composition.png/120px-Pentagon_reflection_composition.png" decoding="async" loading="lazy" width="120" height="30" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/4/48/Pentagon_reflection_composition.png/180px-Pentagon_reflection_composition.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/4/48/Pentagon_reflection_composition.png/240px-Pentagon_reflection_composition.png 2x" data-file-width="523" data-file-height="130" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Pentagon_reflection_composition.png" class="galleryfilename galleryfilename-truncate" title="File:Pentagon reflection composition.png">Pentagon reflection composition.png</a> 523 × 130; 10 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Pentagon_reflection.png" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/61/Pentagon_reflection.png/120px-Pentagon_reflection.png" decoding="async" loading="lazy" width="120" height="48" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/6/61/Pentagon_reflection.png/180px-Pentagon_reflection.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/6/61/Pentagon_reflection.png/240px-Pentagon_reflection.png 2x" data-file-width="321" data-file-height="129" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Pentagon_reflection.png" class="galleryfilename galleryfilename-truncate" title="File:Pentagon reflection.png">Pentagon reflection.png</a> 321 × 129; 6 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Pentagon_rotation.png" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Pentagon_rotation.png/120px-Pentagon_rotation.png" decoding="async" loading="lazy" width="120" height="45" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Pentagon_rotation.png/180px-Pentagon_rotation.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Pentagon_rotation.png/240px-Pentagon_rotation.png 2x" data-file-width="337" data-file-height="126" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Pentagon_rotation.png" class="galleryfilename galleryfilename-truncate" title="File:Pentagon rotation.png">Pentagon rotation.png</a> 337 × 126; 6 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Sphere_symmetry_group_td.png" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Sphere_symmetry_group_td.png/120px-Sphere_symmetry_group_td.png" decoding="async" loading="lazy" width="120" height="116" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Sphere_symmetry_group_td.png/180px-Sphere_symmetry_group_td.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Sphere_symmetry_group_td.png/240px-Sphere_symmetry_group_td.png 2x" data-file-width="649" data-file-height="625" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Sphere_symmetry_group_td.png" class="galleryfilename galleryfilename-truncate" title="File:Sphere symmetry group td.png">Sphere symmetry group td.png</a> 649 × 625; 28 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:T2_tree.svg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/T2_tree.svg/120px-T2_tree.svg.png" decoding="async" loading="lazy" width="120" height="103" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/T2_tree.svg/180px-T2_tree.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/T2_tree.svg/240px-T2_tree.svg.png 2x" data-file-width="373" data-file-height="321" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:T2_tree.svg" class="galleryfilename galleryfilename-truncate" title="File:T2 tree.svg">T2 tree.svg</a> 373 × 321; 10 KB<br> </div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Variante_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Variante_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/120px-Variante_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" decoding="async" loading="lazy" width="120" height="50" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Variante_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/180px-Variante_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Variante_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg/240px-Variante_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg 2x" data-file-width="984" data-file-height="413" /></a></span></div> <div class="gallerytext"><a href="/wiki/File:Variante_de_l%27automate_de_l%27allumeur_de_r%C3%A9verb%C3%A8res.jpg" class="galleryfilename galleryfilename-truncate" title="File:Variante de l'automate de l'allumeur de réverbères.jpg">Variante de l'automate de l'allumeur de réverbères.jpg</a> 984 × 413; 33 KB<br> </div> </li> </ul> </div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://commons.wikimedia.org/w/index.php?title=Category:Geometric_group_theory&oldid=308659594">https://commons.wikimedia.org/w/index.php?title=Category:Geometric_group_theory&oldid=308659594</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categories" title="Special:Categories">Categories</a>: <ul><li><a href="/wiki/Category:Geometry" title="Category:Geometry">Geometry</a></li><li><a href="/wiki/Category:Group_theory" title="Category:Group theory">Group theory</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-user-shown">Non-topical/index: <ul><li><a href="/wiki/Category:Uses_of_Wikidata_Infobox" title="Category:Uses of Wikidata Infobox">Uses of Wikidata Infobox</a></li><li><a href="/wiki/Category:Uses_of_Wikidata_Infobox_with_no_image" title="Category:Uses of Wikidata Infobox with no image">Uses of Wikidata Infobox with no image</a></li></ul></div></div> </div> </div> <div id="mw-navigation"> <h2>Navigation menu</h2> <div id="mw-head"> <nav id="p-personal" class="mw-portlet mw-portlet-personal vector-user-menu-legacy vector-menu" aria-labelledby="p-personal-label" > <h3 id="p-personal-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Personal tools</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-uls" class="mw-list-item active"><a class="uls-trigger" href="#"><span>English</span></a></li><li id="pt-anonuserpage" class="mw-list-item"><span title="The user page for the IP address you are editing as">Not logged in</span></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li><li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-createaccount" class="mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Category%3AGeometric+group+theory" title="You are encouraged to create an account and log in; however, it is not mandatory"><span>Create account</span></a></li><li id="pt-login" class="mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Category%3AGeometric+group+theory" title="You are encouraged to log in; however, it is not mandatory [o]" accesskey="o"><span>Log in</span></a></li> </ul> </div> </nav> <div id="left-navigation"> <nav id="p-namespaces" class="mw-portlet mw-portlet-namespaces vector-menu-tabs vector-menu-tabs-legacy vector-menu" aria-labelledby="p-namespaces-label" > <h3 id="p-namespaces-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Namespaces</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-category" class="selected mw-list-item"><a href="/wiki/Category:Geometric_group_theory" title="View the category page [c]" accesskey="c"><span>Category</span></a></li><li id="ca-talk" class="new mw-list-item"><a href="/w/index.php?title=Category_talk:Geometric_group_theory&action=edit&redlink=1" rel="discussion" class="new" title="Discussion about the content page (page does not exist) [t]" accesskey="t"><span>Discussion</span></a></li> </ul> </div> </nav> <nav id="p-variants" class="mw-portlet mw-portlet-variants emptyPortlet vector-menu-dropdown vector-menu" aria-labelledby="p-variants-label" > <input type="checkbox" id="p-variants-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-variants" class="vector-menu-checkbox" aria-labelledby="p-variants-label" > <label id="p-variants-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">English</span> </label> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </nav> </div> <div id="right-navigation"> <nav id="p-views" class="mw-portlet mw-portlet-views vector-menu-tabs vector-menu-tabs-legacy vector-menu" aria-labelledby="p-views-label" > <h3 id="p-views-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Views</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected mw-list-item"><a href="/wiki/Category:Geometric_group_theory"><span>View</span></a></li><li id="ca-edit" class="mw-list-item"><a href="/w/index.php?title=Category:Geometric_group_theory&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="mw-list-item"><a href="/w/index.php?title=Category:Geometric_group_theory&action=history" title="Past revisions of this page [h]" accesskey="h"><span>History</span></a></li> </ul> </div> </nav> <nav id="p-cactions" class="mw-portlet mw-portlet-cactions emptyPortlet vector-menu-dropdown vector-menu" aria-labelledby="p-cactions-label" title="More options" > <input type="checkbox" id="p-cactions-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-cactions" class="vector-menu-checkbox" aria-labelledby="p-cactions-label" > <label id="p-cactions-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">More</span> </label> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </nav> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box"> <h3 >Search</h3> <form action="/w/index.php" id="searchform" class="vector-search-box-form"> <div id="simpleSearch" class="vector-search-box-inner" data-search-loc="header-navigation"> <input class="vector-search-box-input" type="search" name="search" placeholder="Search Wikimedia Commons" aria-label="Search Wikimedia Commons" autocapitalize="sentences" title="Search Wikimedia Commons [f]" accesskey="f" id="searchInput" > <input type="hidden" name="title" value="Special:MediaSearch"> <input id="mw-searchButton" class="searchButton mw-fallbackSearchButton" type="submit" name="fulltext" title="Search the pages for this text" value="Search"> <input id="searchButton" class="searchButton" type="submit" name="go" title="Go to a page with this exact name if it exists" value="Go"> </div> </form> </div> </div> </div> <div id="mw-panel" class="vector-legacy-sidebar"> <div id="p-logo" role="banner"> <a class="mw-wiki-logo" href="/wiki/Main_Page" title="Visit the main page"></a> </div> <nav id="p-navigation" class="mw-portlet mw-portlet-navigation vector-menu-portal portal vector-menu" aria-labelledby="p-navigation-label" > <h3 id="p-navigation-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Navigate</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-welcome" class="mw-list-item"><a href="/wiki/Commons:Welcome"><span>Welcome</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Commons:Community_portal" title="About the project, what you can do, where to find things"><span>Community portal</span></a></li><li id="n-village-pump" class="mw-list-item"><a href="/wiki/Commons:Village_pump"><span>Village pump</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Special:MyLanguage/Help:Contents" title="The place to find out"><span>Help center</span></a></li> </ul> </div> </nav> <nav id="p-participate" class="mw-portlet mw-portlet-participate vector-menu-portal portal vector-menu" aria-labelledby="p-participate-label" > <h3 id="p-participate-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Participate</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-uploadbtn" class="mw-list-item"><a href="/wiki/Special:UploadWizard"><span>Upload file</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes in the wiki [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-latestfiles" class="mw-list-item"><a href="/wiki/Special:NewFiles"><span>Latest files</span></a></li><li id="n-randomimage" class="mw-list-item"><a href="/wiki/Special:Random/File" title="Load a random file [x]" accesskey="x"><span>Random file</span></a></li><li id="n-contact" class="mw-list-item"><a href="/wiki/Commons:Contact_us"><span>Contact us</span></a></li> </ul> </div> </nav> <nav id="p-tb" class="mw-portlet mw-portlet-tb vector-menu-portal portal vector-menu" aria-labelledby="p-tb-label" > <h3 id="p-tb-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Tools</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Category:Geometric_group_theory" title="A list of all wiki pages that link here [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Category:Geometric_group_theory" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Category:Geometric_group_theory&oldid=308659594" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Category:Geometric_group_theory&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fcommons.wikimedia.org%2Fwiki%2FCategory%3AGeometric_group_theory"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fcommons.wikimedia.org%2Fwiki%2FCategory%3AGeometric_group_theory"><span>Download QR code</span></a></li> </ul> </div> </nav> <nav id="p-coll-print_export" class="mw-portlet mw-portlet-coll-print_export vector-menu-portal portal vector-menu" aria-labelledby="p-coll-print_export-label" > <h3 id="p-coll-print_export-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Print/export</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Special:Book&bookcmd=book_creator&referer=Category%3AGeometric+group+theory"><span>Create a book</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Category%3AGeometric_group_theory&action=show-download-screen"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Category:Geometric_group_theory&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </nav> <nav id="p-wikibase-otherprojects" class="mw-portlet mw-portlet-wikibase-otherprojects vector-menu-portal portal vector-menu" aria-labelledby="p-wikibase-otherprojects-label" > <h3 id="p-wikibase-otherprojects-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">In other projects</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-wikipedia mw-list-item"><a href="https://en.wikipedia.org/wiki/Category:Geometric_group_theory" hreflang="en"><span>Wikipedia</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q8488080" title="Link to connected data repository item [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </nav> <nav id="p-lang" class="mw-portlet mw-portlet-lang vector-menu-portal portal vector-menu" aria-labelledby="p-lang-label" > <h3 id="p-lang-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">In Wikipedia</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D8%B2%D9%85%D8%B1_%D8%A7%D9%84%D9%87%D9%86%D8%AF%D8%B3%D9%8A%D8%A9" title="نظرية الزمر الهندسية – Arabic" lang="ar" hreflang="ar" data-title="نظرية الزمر الهندسية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Geometrische_Gruppentheorie" title="Geometrische Gruppentheorie – German" lang="de" hreflang="de" data-title="Geometrische Gruppentheorie" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%B9%CE%BA%CE%AE_%CE%B8%CE%B5%CF%89%CF%81%CE%AF%CE%B1_%CE%BF%CE%BC%CE%AC%CE%B4%CF%89%CE%BD" title="Γεωμετρική θεωρία ομάδων – Greek" lang="el" hreflang="el" data-title="Γεωμετρική θεωρία ομάδων" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Geometric_group_theory" title="Geometric group theory – English" lang="en" hreflang="en" data-title="Geometric group theory" data-language-autonym="English" data-language-local-name="English" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kategorio:Geometria_grupo-teorio" title="Kategorio:Geometria grupo-teorio – Esperanto" lang="eo" hreflang="eo" data-title="Kategorio:Geometria grupo-teorio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Teor%C3%ADa_geom%C3%A9trica_de_grupos" title="Teoría geométrica de grupos – Spanish" lang="es" hreflang="es" data-title="Teoría geométrica de grupos" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%AF%D9%87:%D9%86%D8%B8%D8%B1%DB%8C%D9%87_%DA%AF%D8%B1%D9%88%D9%87%E2%80%8C%D9%87%D8%A7%DB%8C_%D9%87%D9%86%D8%AF%D8%B3%DB%8C" title="رده:نظریه گروه‌های هندسی – Persian" lang="fa" hreflang="fa" data-title="رده:نظریه گروه‌های هندسی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Th%C3%A9orie_g%C3%A9om%C3%A9trique_des_groupes" title="Théorie géométrique des groupes – French" lang="fr" hreflang="fr" data-title="Théorie géométrique des groupes" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%97%D7%91%D7%95%D7%A8%D7%95%D7%AA_%D7%94%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%AA" title="קטגוריה:תורת החבורות הגאומטרית – Hebrew" lang="he" hreflang="he" data-title="קטגוריה:תורת החבורות הגאומטרית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%B9%BE%E4%BD%95%E5%AD%A6%E7%9A%84%E7%BE%A4%E8%AB%96" title="幾何学的群論 – Japanese" lang="ja" hreflang="ja" data-title="幾何学的群論" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B6%84%EB%A5%98:%EA%B8%B0%ED%95%98%EA%B5%B0%EB%A1%A0" title="분류:기하군론 – Korean" lang="ko" hreflang="ko" data-title="분류:기하군론" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Meetkundige_groepentheorie" title="Meetkundige groepentheorie – Dutch" lang="nl" hreflang="nl" data-title="Meetkundige groepentheorie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Teoria_geom%C3%A9trica_de_grupos" title="Teoria geométrica de grupos – Portuguese" lang="pt" hreflang="pt" data-title="Teoria geométrica de grupos" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Teoria_geometric%C4%83_a_grupurilor" title="Teoria geometrică a grupurilor – Romanian" lang="ro" hreflang="ro" data-title="Teoria geometrică a grupurilor" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%B3%D1%80%D1%83%D0%BF%D0%BF" title="Геометрическая теория групп – Russian" lang="ru" hreflang="ru" data-title="Геометрическая теория групп" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kategorija:Geometri%C4%8Dna_teorija_grup" title="Kategorija:Geometrična teorija grup – Slovenian" lang="sl" hreflang="sl" data-title="Kategorija:Geometrična teorija grup" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kategori:Geometrisk_gruppteori" title="Kategori:Geometrisk gruppteori – Swedish" lang="sv" hreflang="sv" data-title="Kategori:Geometrisk gruppteori" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B0_%D1%82%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B3%D1%80%D1%83%D0%BF" title="Геометрична теорія груп – Ukrainian" lang="uk" hreflang="uk" data-title="Геометрична теорія груп" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%C3%BD_thuy%E1%BA%BFt_nh%C3%B3m_h%C3%ACnh_h%E1%BB%8Dc" title="Lý thuyết nhóm hình học – Vietnamese" lang="vi" hreflang="vi" data-title="Lý thuyết nhóm hình học" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/Category:%E5%B9%BE%E4%BD%95%E7%BE%A3%E8%AB%96" title="Category:幾何羣論 – Cantonese" lang="yue" hreflang="yue" data-title="Category:幾何羣論" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%87%A0%E4%BD%95%E7%BE%A4%E8%AE%BA" title="几何群论 – Chinese" lang="zh" hreflang="zh" data-title="几何群论" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%B9%BE%E4%BD%95%E7%BE%A3%E8%AB%96" title="幾何羣論 – Cantonese" lang="yue" hreflang="yue" data-title="幾何羣論" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q8488080#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </nav> </div> </div> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 29 June 2018, at 23:25.</li> <li id="footer-info-copyright">Files are available under licenses specified on their description page. All structured data from the file namespace is available under the <a rel="nofollow" class="external text" href="https://creativecommons.org/publicdomain/zero/1.0/">Creative Commons CC0 License</a>; all unstructured text is available under the <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-ShareAlike License</a>; additional terms may apply. By using this site, you agree to the <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">Terms of Use</a> and the <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy Policy</a>.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Commons:Welcome">About Wikimedia Commons</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Commons:General_disclaimer">Disclaimers</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/commons.wikimedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//commons.m.wikimedia.org/w/index.php?title=Category:Geometric_group_theory&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> <script>(RLQ=window.RLQ||[]).push(function(){mw.log.warn("This page is using the deprecated ResourceLoader module \"codex-search-styles\".\n[1.43] Use a CodexModule with codexComponents to set your specific components used: https://www.mediawiki.org/wiki/Codex#Using_a_limited_subset_of_components");mw.config.set({"wgHostname":"mw-web.codfw.main-6b8d669998-cpdg4","wgBackendResponseTime":461,"wgPageParseReport":{"limitreport":{"cputime":"0.148","walltime":"0.273","ppvisitednodes":{"value":120,"limit":1000000},"postexpandincludesize":{"value":23242,"limit":2097152},"templateargumentsize":{"value":27,"limit":2097152},"expansiondepth":{"value":8,"limit":100},"expensivefunctioncount":{"value":3,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":2687,"limit":5000000},"entityaccesscount":{"value":4,"limit":400},"timingprofile":["100.00% 251.999 1 -total","100.00% 251.999 1 Template:Wikidata_Infobox"," 89.70% 226.038 1 Template:Wikidata_Infobox/core"]},"scribunto":{"limitreport-timeusage":{"value":"0.076","limit":"10.000"},"limitreport-memusage":{"value":2135580,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-6b8d669998-cpdg4","timestamp":"20241128052851","ttl":2592000,"transientcontent":false}}});});</script> </body> </html>