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class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Projekt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Obsah" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Obsah</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrýt</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(úvod)</div> </a> </li> <li id="toc-Historie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historie"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Historie</span> </div> </a> <ul id="toc-Historie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Grupa" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Grupa"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Grupa</span> </div> </a> <ul id="toc-Grupa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Důležité_věty_teorie_grup" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Důležité_věty_teorie_grup"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Důležité věty teorie grup</span> </div> </a> <ul id="toc-Důležité_věty_teorie_grup-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Odkazy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Odkazy</span> </div> </a> <button aria-controls="toc-Odkazy-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Přepnout podsekci Odkazy</span> </button> <ul id="toc-Odkazy-sublist" class="vector-toc-list"> <li id="toc-Související_články" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Související_články"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Související články</span> </div> </a> <ul id="toc-Související_články-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externí_odkazy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Externí_odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Externí odkazy</span> </div> </a> <ul id="toc-Externí_odkazy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Literatura" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Literatura"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Literatura</span> </div> </a> <ul id="toc-Literatura-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Obsah" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Přepnout obsah" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Přepnout obsah</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Teorie grup</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Přejděte k článku v jiném jazyce. Je dostupný v 72 jazycích" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-72" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">72 jazyků</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Teor%C3%ADa_de_grupos" title="Teoría de grupos – aragonština" lang="an" hreflang="an" data-title="Teoría de grupos" data-language-autonym="Aragonés" data-language-local-name="aragonština" class="interlanguage-link-target"><span>Aragonés</span></a></li><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" title="نظرية الزمر – arabština" lang="ar" hreflang="ar" data-title="نظرية الزمر" data-language-autonym="العربية" data-language-local-name="arabština" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Teor%C3%ADa_de_grupos" title="Teoría de grupos – asturština" lang="ast" hreflang="ast" data-title="Teoría de grupos" data-language-autonym="Asturianu" data-language-local-name="asturština" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Qrup_n%C9%99z%C9%99riyy%C9%99si" title="Qrup nəzəriyyəsi – ázerbájdžánština" lang="az" hreflang="az" data-title="Qrup nəzəriyyəsi" data-language-autonym="Azərbaycanca" data-language-local-name="ázerbájdžánština" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A2%D3%A9%D1%80%D0%BA%D3%A9%D0%BC%D0%B4%D3%99%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D2%BB%D1%8B" title="Төркөмдәр теорияһы – baškirština" lang="ba" hreflang="ba" data-title="Төркөмдәр теорияһы" data-language-autonym="Башҡортса" data-language-local-name="baškirština" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Gropiu_teuor%C4%97j%C4%97" title="Gropiu teuorėjė – žemaitština" lang="sgs" hreflang="sgs" data-title="Gropiu teuorėjė" data-language-autonym="Žemaitėška" data-language-local-name="žemaitština" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%B3%D1%80%D1%83%D0%BF" title="Тэорыя груп – běloruština" lang="be" hreflang="be" data-title="Тэорыя груп" data-language-autonym="Беларуская" data-language-local-name="běloruština" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%B3%D1%80%D1%83%D0%BF%D0%B0%D1%9E" title="Тэорыя групаў – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Тэорыя групаў" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%B3%D1%80%D1%83%D0%BF%D0%B8%D1%82%D0%B5" title="Теория на групите – bulharština" lang="bg" hreflang="bg" data-title="Теория на групите" data-language-autonym="Български" data-language-local-name="bulharština" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Damkaniezh_ar_strollo%C3%B9" title="Damkaniezh ar strolloù – bretonština" lang="br" hreflang="br" data-title="Damkaniezh ar strolloù" data-language-autonym="Brezhoneg" data-language-local-name="bretonština" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Teorija_grupa" title="Teorija grupa – bosenština" lang="bs" hreflang="bs" data-title="Teorija grupa" data-language-autonym="Bosanski" data-language-local-name="bosenština" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Teoria_de_grups" title="Teoria de grups – katalánština" lang="ca" hreflang="ca" data-title="Teoria de grups" data-language-autonym="Català" data-language-local-name="katalánština" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%DB%8C%DB%86%D8%B1%DB%8C%DB%8C_%DA%AF%D8%B1%D9%88%D9%88%D9%BE" title="تیۆریی گرووپ – kurdština (sorání)" lang="ckb" hreflang="ckb" data-title="تیۆریی گرووپ" data-language-autonym="کوردی" data-language-local-name="kurdština (sorání)" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A3%D1%88%D0%BA%C4%83%D0%BD%D1%81%D0%B5%D0%BD_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D0%B9%C4%95" title="Ушкăнсен теорийĕ – čuvaština" lang="cv" hreflang="cv" data-title="Ушкăнсен теорийĕ" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Damcaniaeth_grwpiau" title="Damcaniaeth grwpiau – velština" lang="cy" hreflang="cy" data-title="Damcaniaeth grwpiau" data-language-autonym="Cymraeg" data-language-local-name="velština" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Gruppeteori_(matematik)" title="Gruppeteori (matematik) – dánština" lang="da" hreflang="da" data-title="Gruppeteori (matematik)" data-language-autonym="Dansk" data-language-local-name="dánština" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Gruppentheorie" title="Gruppentheorie – němčina" lang="de" hreflang="de" data-title="Gruppentheorie" data-language-autonym="Deutsch" data-language-local-name="němčina" 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%98%CE%B5%CF%89%CF%81%CE%AF%CE%B1_%CE%BF%CE%BC%CE%AC%CE%B4%CF%89%CE%BD" title="Θεωρία ομάδων – řečtina" lang="el" hreflang="el" data-title="Θεωρία ομάδων" data-language-autonym="Ελληνικά" data-language-local-name="řečtina" 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/Group_theory" title="Group theory – angličtina" lang="en" hreflang="en" data-title="Group theory" data-language-autonym="English" data-language-local-name="angličtina" 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/Grupo-teorio" title="Grupo-teorio – esperanto" lang="eo" hreflang="eo" data-title="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_de_grupos" title="Teoría de grupos – španělština" lang="es" hreflang="es" data-title="Teoría de grupos" data-language-autonym="Español" data-language-local-name="španělština" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Talde-teoria" title="Talde-teoria – baskičtina" lang="eu" hreflang="eu" data-title="Talde-teoria" data-language-autonym="Euskara" data-language-local-name="baskičtina" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%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" title="نظریه گروه‌ها – perština" lang="fa" hreflang="fa" data-title="نظریه گروه‌ها" data-language-autonym="فارسی" data-language-local-name="perština" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Ryhm%C3%A4teoria" title="Ryhmäteoria – finština" lang="fi" hreflang="fi" data-title="Ryhmäteoria" data-language-autonym="Suomi" data-language-local-name="finština" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Th%C3%A9orie_des_groupes" title="Théorie des groupes – francouzština" lang="fr" hreflang="fr" data-title="Théorie des groupes" data-language-autonym="Français" data-language-local-name="francouzština" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fur mw-list-item"><a href="https://fur.wikipedia.org/wiki/Teorie_dai_grups" title="Teorie dai grups – furlanština" lang="fur" hreflang="fur" data-title="Teorie dai grups" data-language-autonym="Furlan" data-language-local-name="furlanština" class="interlanguage-link-target"><span>Furlan</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Teor%C3%ADa_de_grupos" title="Teoría de grupos – galicijština" lang="gl" hreflang="gl" data-title="Teoría de grupos" data-language-autonym="Galego" data-language-local-name="galicijština" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%97%D7%91%D7%95%D7%A8%D7%95%D7%AA" title="תורת החבורות – hebrejština" lang="he" hreflang="he" data-title="תורת החבורות" data-language-autonym="עברית" data-language-local-name="hebrejština" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%AE%E0%A5%82%E0%A4%B9_%E0%A4%B8%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%BE%E0%A4%82%E0%A4%A4" title="समूह सिद्धांत – hindština" lang="hi" hreflang="hi" data-title="समूह सिद्धांत" data-language-autonym="हिन्दी" data-language-local-name="hindština" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Teorija_grupa" title="Teorija grupa – chorvatština" lang="hr" hreflang="hr" data-title="Teorija grupa" data-language-autonym="Hrvatski" data-language-local-name="chorvatština" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Csoportelm%C3%A9let" title="Csoportelmélet – maďarština" lang="hu" hreflang="hu" data-title="Csoportelmélet" data-language-autonym="Magyar" data-language-local-name="maďarština" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Theoria_de_gruppos" title="Theoria de gruppos – interlingua" lang="ia" hreflang="ia" data-title="Theoria de gruppos" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Teori_grup" title="Teori grup – indonéština" lang="id" hreflang="id" data-title="Teori grup" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéština" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Teoria_dei_gruppi" title="Teoria dei gruppi – italština" lang="it" hreflang="it" data-title="Teoria dei gruppi" data-language-autonym="Italiano" data-language-local-name="italština" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%BE%A4%E8%AB%96" title="群論 – japonština" lang="ja" hreflang="ja" data-title="群論" data-language-autonym="日本語" data-language-local-name="japonština" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AF%E1%83%92%E1%83%A3%E1%83%A4%E1%83%97%E1%83%90_%E1%83%97%E1%83%94%E1%83%9D%E1%83%A0%E1%83%98%E1%83%90" title="ჯგუფთა თეორია – gruzínština" lang="ka" hreflang="ka" data-title="ჯგუფთა თეორია" data-language-autonym="ქართული" data-language-local-name="gruzínština" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B5%B0%EB%A1%A0" title="군론 – korejština" lang="ko" hreflang="ko" data-title="군론" data-language-autonym="한국어" data-language-local-name="korejština" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Theoria_catervarum" title="Theoria catervarum – latina" lang="la" hreflang="la" data-title="Theoria catervarum" data-language-autonym="Latina" data-language-local-name="latina" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Grupu_teorija" title="Grupu teorija – lotyština" lang="lv" hreflang="lv" data-title="Grupu teorija" data-language-autonym="Latviešu" data-language-local-name="lotyština" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Teori_kumpulan" title="Teori kumpulan – malajština" lang="ms" hreflang="ms" data-title="Teori kumpulan" data-language-autonym="Bahasa Melayu" data-language-local-name="malajština" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%97%E0%A5%8D%E0%A4%B0%E0%A5%81%E0%A4%AA_%E0%A4%B8%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A4" title="ग्रुप सिद्धान्त – névárština" lang="new" hreflang="new" data-title="ग्रुप सिद्धान्त" data-language-autonym="नेपाल भाषा" data-language-local-name="névárština" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Groepentheorie" title="Groepentheorie – nizozemština" lang="nl" hreflang="nl" data-title="Groepentheorie" data-language-autonym="Nederlands" data-language-local-name="nizozemština" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Gruppeteori" title="Gruppeteori – norština (nynorsk)" lang="nn" hreflang="nn" data-title="Gruppeteori" data-language-autonym="Norsk nynorsk" data-language-local-name="norština (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Gruppeteori" title="Gruppeteori – norština (bokmål)" lang="nb" hreflang="nb" data-title="Gruppeteori" data-language-autonym="Norsk bokmål" data-language-local-name="norština (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%97%E0%A8%B0%E0%A9%81%E0%A9%B1%E0%A8%AA_%E0%A8%A5%E0%A8%BF%E0%A8%8A%E0%A8%B0%E0%A9%80" title="ਗਰੁੱਪ ਥਿਊਰੀ – paňdžábština" lang="pa" hreflang="pa" data-title="ਗਰੁੱਪ ਥਿਊਰੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="paňdžábština" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Teoria_grup" title="Teoria grup – polština" lang="pl" hreflang="pl" data-title="Teoria grup" data-language-autonym="Polski" data-language-local-name="polština" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%B9%D9%88%D9%84%DB%8C_%D8%B3%D9%88%DA%86" title="ٹولی سوچ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ٹولی سوچ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Teoria_dos_grupos" title="Teoria dos grupos – portugalština" lang="pt" hreflang="pt" data-title="Teoria dos grupos" data-language-autonym="Português" data-language-local-name="portugalština" 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_grupurilor" title="Teoria grupurilor – rumunština" lang="ro" hreflang="ro" data-title="Teoria grupurilor" data-language-autonym="Română" data-language-local-name="rumunština" 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%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%B3%D1%80%D1%83%D0%BF%D0%BF" title="Теория групп – ruština" lang="ru" hreflang="ru" data-title="Теория групп" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D2%91%D1%80%D1%83%D0%BF" title="Теорія ґруп – rusínština" lang="rue" hreflang="rue" data-title="Теорія ґруп" data-language-autonym="Русиньскый" data-language-local-name="rusínština" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Group_theory" title="Group theory – skotština" lang="sco" hreflang="sco" data-title="Group theory" data-language-autonym="Scots" data-language-local-name="skotština" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Teorija_grupa" title="Teorija grupa – srbochorvatština" lang="sh" hreflang="sh" data-title="Teorija grupa" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvatština" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Group_theory" title="Group theory – Simple English" lang="en-simple" hreflang="en-simple" data-title="Group theory" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Te%C3%B3ria_gr%C3%BAp" title="Teória grúp – slovenština" lang="sk" hreflang="sk" data-title="Teória grúp" data-language-autonym="Slovenčina" data-language-local-name="slovenština" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Teorija_grup" title="Teorija grup – slovinština" lang="sl" hreflang="sl" data-title="Teorija grup" data-language-autonym="Slovenščina" data-language-local-name="slovinština" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Teoria_e_grupeve" title="Teoria e grupeve – albánština" lang="sq" hreflang="sq" data-title="Teoria e grupeve" data-language-autonym="Shqip" data-language-local-name="albánština" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%B3%D1%80%D1%83%D0%BF%D0%B0" title="Теорија група – srbština" lang="sr" hreflang="sr" data-title="Теорија група" data-language-autonym="Српски / srpski" data-language-local-name="srbština" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Gruppteori" title="Gruppteori – švédština" lang="sv" hreflang="sv" data-title="Gruppteori" data-language-autonym="Svenska" data-language-local-name="švédština" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%81%E0%AE%B2%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AF%8B%E0%AE%9F%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%81" title="குலக் கோட்பாடு – tamilština" lang="ta" hreflang="ta" data-title="குலக் கோட்பாடு" data-language-autonym="தமிழ்" data-language-local-name="tamilština" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%81%E0%B8%A3%E0%B8%B8%E0%B8%9B" title="ทฤษฎีกรุป – thajština" lang="th" hreflang="th" data-title="ทฤษฎีกรุป" data-language-autonym="ไทย" data-language-local-name="thajština" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Teorya_ng_grupo" title="Teorya ng grupo – tagalog" lang="tl" hreflang="tl" data-title="Teorya ng grupo" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Grup_teorisi" title="Grup teorisi – turečtina" lang="tr" hreflang="tr" data-title="Grup teorisi" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B3%D1%80%D1%83%D0%BF" title="Теорія груп – ukrajinština" lang="uk" hreflang="uk" data-title="Теорія груп" data-language-autonym="Українська" data-language-local-name="ukrajinština" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%DB%8C%DB%82_%DA%AF%D8%B1%D9%88%DB%81" title="نظریۂ گروہ – urdština" lang="ur" hreflang="ur" data-title="نظریۂ گروہ" data-language-autonym="اردو" data-language-local-name="urdština" class="interlanguage-link-target"><span>اردو</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" title="Lý thuyết nhóm – vietnamština" lang="vi" hreflang="vi" data-title="Lý thuyết nhóm" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamština" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Teyorya_grupo" title="Teyorya grupo – warajština" lang="war" hreflang="war" data-title="Teyorya grupo" data-language-autonym="Winaray" data-language-local-name="warajština" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%BE%A4%E8%AE%BA" title="群论 – čínština (dialekty Wu)" lang="wuu" hreflang="wuu" data-title="群论" data-language-autonym="吴语" data-language-local-name="čínština (dialekty Wu)" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%92%D7%A8%D7%95%D7%A4%D7%A2_%D7%98%D7%A2%D7%90%D7%A8%D7%99%D7%A2" title="גרופע טעאריע – jidiš" lang="yi" hreflang="yi" data-title="גרופע טעאריע" data-language-autonym="ייִדיש" data-language-local-name="jidiš" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%BE%A4%E8%AE%BA" title="群论 – čínština" lang="zh" hreflang="zh" data-title="群论" data-language-autonym="中文" data-language-local-name="čínština" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/K%C3%BBn-l%C5%ABn" title="Kûn-lūn – čínština (dialekty Minnan)" lang="nan" hreflang="nan" data-title="Kûn-lūn" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="čínština (dialekty Minnan)" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%BE%A3%E8%AB%96" title="羣論 – kantonština" lang="yue" 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id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="cs" dir="ltr"><p><b>Teorie grup</b> je <a href="/wiki/Matematika" title="Matematika">matematická</a> disciplína zabývající se studiem <a href="/wiki/Grupa" title="Grupa">grup</a>. Jde o podobor <a href="/wiki/Algebra" title="Algebra">algebry</a>. Má mnoho aplikací v celé matematice i v dalších oborech – <a href="/wiki/Fyzika" title="Fyzika">fyzice</a>, <a href="/wiki/Informatika" title="Informatika">informatice</a> či <a href="/wiki/Chemie" title="Chemie">chemii</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historie">Historie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorie_grup&veaction=edit&section=1" title="Editace sekce: Historie" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorie_grup&action=edit&section=1" title="Editovat zdrojový kód sekce Historie"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Počátky teorie grup sahají do posledních let <a href="/wiki/18._stolet%C3%AD" title="18. století">18.</a> a počátku <a href="/wiki/19._stolet%C3%AD" title="19. století">19. století</a>, kdy se začala vyvíjet jako důsledek rozvoje teorie <a href="/wiki/Algebraick%C3%A1_rovnice" class="mw-redirect" title="Algebraická rovnice">algebraických rovnic</a>, <a href="/wiki/Teorie_%C4%8D%C3%ADsel" title="Teorie čísel">teorie čísel</a> a <a href="/wiki/Geometrie" title="Geometrie">geometrie</a>. Prvními matematiky, kteří se zabývali touto oblastí byli <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a>, <a href="/wiki/Joseph_Louis_Lagrange" class="mw-redirect" title="Joseph Louis Lagrange">Joseph Louis Lagrange</a>, <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a>, <a href="/wiki/Niels_Henrik_Abel" title="Niels Henrik Abel">Niels Henrik Abel</a> a <a href="/wiki/%C3%89variste_Galois" title="Évariste Galois">Évariste Galois</a>. </p><p>Moderní definici grupy podal roku <a href="/wiki/1882" title="1882">1882</a> <a href="/w/index.php?title=Walther_von_Dyck&action=edit&redlink=1" class="new" title="Walther von Dyck (stránka neexistuje)">Walther von Dyck</a>. </p> <table class="noprint metadata plainlinks sectstub" cellpadding="2" style="background: transparent;"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/Soubor:Wiki_letter_w.svg" class="mw-file-description" title="Pahýl"><img alt="Pahýl" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/25px-Wiki_letter_w.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/38px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/50px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a></span> </td> <td><i>Tato část článku je příliš stručná nebo <a href="/wiki/Wikipedie:Pah%C3%BDl" title="Wikipedie:Pahýl">postrádá důležité informace</a>. Pomozte Wikipedii tím, že ji vhodně <a class="external text" href="https://cs.wikipedia.org/w/index.php?title=Teorie_grup&action=edit">rozšíříte</a>.</i> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Grupa">Grupa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorie_grup&veaction=edit&section=2" title="Editace sekce: Grupa" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorie_grup&action=edit&section=2" title="Editovat zdrojový kód sekce Grupa"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="uvodni-upozorneni hatnote">Související informace naleznete také v článku <a href="/wiki/Grupa" title="Grupa">Grupa</a>.</div> <p><a href="/wiki/Grupa" title="Grupa">Grupa</a> je základním pojmem teorie grup. Je definována jako <a href="/wiki/Mno%C5%BEina" title="Množina">množina</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {G} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">G</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {G} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6df6ffb3d7e5214ab2f1d7c5b3915ca050523cf9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \mathbb {G} }"></span> spolu s <a href="/wiki/Bin%C3%A1rn%C3%AD_operace" title="Binární operace">binární operací</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cdot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⋅</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cdot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba2c023bad1bd39ed49080f729cbf26bc448c9ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.439ex; margin-bottom: -0.61ex; width:0.647ex; height:1.176ex;" alt="{\displaystyle \cdot }"></span> splňující tři grupové axiomy: </p> <dl><dd><table cellpadding="5"> <tbody><tr> <td><a href="/wiki/Asociativita" title="Asociativita">Asociativita</a>: </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f\cdot (g\cdot h)=(f\cdot g)\cdot h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo>⋅</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>f</mi> <mo>⋅</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f\cdot (g\cdot h)=(f\cdot g)\cdot h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0074ad95649d6dc755fd074016eb671ded30c3f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.901ex; height:2.843ex;" alt="{\displaystyle f\cdot (g\cdot h)=(f\cdot g)\cdot h}"></span> </td></tr> <tr> <td>Existence neutrálního prvku: </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\exists e)(\forall g)\quad g\cdot e=e\cdot g=g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi mathvariant="normal">∃</mi> <mi>e</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">∀</mi> <mi>g</mi> <mo stretchy="false">)</mo> <mspace width="1em" /> <mi>g</mi> <mo>⋅</mo> <mi>e</mi> <mo>=</mo> <mi>e</mi> <mo>⋅</mo> <mi>g</mi> <mo>=</mo> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\exists e)(\forall g)\quad g\cdot e=e\cdot g=g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce5fe659062287b5c29e279f02f1e708f2d2834b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.796ex; height:2.843ex;" alt="{\displaystyle (\exists e)(\forall g)\quad g\cdot e=e\cdot g=g}"></span> </td></tr> <tr> <td>Existence inverzních prvků: </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\forall g)(\exists h)\quad g\cdot h=h\cdot g=e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi mathvariant="normal">∀</mi> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">∃</mi> <mi>h</mi> <mo stretchy="false">)</mo> <mspace width="1em" /> <mi>g</mi> <mo>⋅</mo> <mi>h</mi> <mo>=</mo> <mi>h</mi> <mo>⋅</mo> <mi>g</mi> <mo>=</mo> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\forall g)(\exists h)\quad g\cdot h=h\cdot g=e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7feaf921ea738fca10e6698d547ed8e320130016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.53ex; height:2.843ex;" alt="{\displaystyle (\forall g)(\exists h)\quad g\cdot h=h\cdot g=e}"></span> </td></tr></tbody></table></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Důležité_věty_teorie_grup"><span id="D.C5.AFle.C5.BEit.C3.A9_v.C4.9Bty_teorie_grup"></span>Důležité věty teorie grup</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorie_grup&veaction=edit&section=3" title="Editace sekce: Důležité věty teorie grup" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorie_grup&action=edit&section=3" title="Editovat zdrojový kód sekce Důležité věty teorie grup"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><b><a href="/wiki/Lagrangeova_v%C4%9Bta_(teorie_grup)" title="Lagrangeova věta (teorie grup)">Lagrangeova věta</a></b>: Je-li <i>G</i> konečná <a href="/wiki/Grupa" title="Grupa">grupa</a> a <i>H</i> její <a href="/wiki/Podgrupa" title="Podgrupa">podgrupa</a>, pak <a href="/wiki/%C5%98%C3%A1d_grupy" class="mw-redirect" title="Řád grupy">řád</a> <i>H</i> dělí řád <i>G</i>.</li> <li><b><a href="/w/index.php?title=Cayleyho_v%C4%9Bta&action=edit&redlink=1" class="new" title="Cayleyho věta (stránka neexistuje)">Cayleyho věta</a></b>: Každá grupa <i>G</i> je <a href="/wiki/Izomorfismus" title="Izomorfismus">izomorfní</a> podgrupě grupy permutací na <i>G</i> (<a href="/wiki/Symetrick%C3%A1_grupa" title="Symetrická grupa">symetrické grupě</a>).</li> <li><b><a href="/wiki/Sylowovy_v%C4%9Bty" title="Sylowovy věty">Sylowovy věty</a></b>: Popisují existenci a vlastnosti <a href="/wiki/P-grupa" title="P-grupa">p-podgrup</a> konečné grupy.</li> <li><b><a href="/wiki/V%C4%9Bta_o_homomorfismu" title="Věta o homomorfismu">Věta o homomorfismu</a></b>: Dává do souvislosti dvě grupy, mezi nimiž je <a href="/wiki/Homomorfismus" title="Homomorfismus">homomorfismus</a>, s jeho <a href="/wiki/J%C3%A1dro_homomorfismu" class="mw-redirect" title="Jádro homomorfismu">jádrem</a> a obrazem.</li> <li><b><a href="/w/index.php?title=Jordan-H%C3%B6lderova_v%C4%9Bta&action=edit&redlink=1" class="new" title="Jordan-Hölderova věta (stránka neexistuje)">Jordan-Hölderova věta</a></b>: Každé dvě <a href="/w/index.php?title=Kompozi%C4%8Dn%C3%AD_%C5%99ada&action=edit&redlink=1" class="new" title="Kompoziční řada (stránka neexistuje)">kompoziční řady</a> dané grupy jsou izomorfní.</li> <li><b><a href="/w/index.php?title=Krull-Schmidtova_v%C4%9Bta&action=edit&redlink=1" class="new" title="Krull-Schmidtova věta (stránka neexistuje)">Krull-Schmidtova věta</a></b>: Stanovuje podmínky pro to, aby grupa <i>G</i> byla konečným <a href="/w/index.php?title=Sou%C4%8Din_grup&action=edit&redlink=1" class="new" title="Součin grup (stránka neexistuje)">součinem</a> svých <a href="/w/index.php?title=Nerozlo%C5%BEiteln%C3%A1_grupa&action=edit&redlink=1" class="new" title="Nerozložitelná grupa (stránka neexistuje)">nerozložitelných podgrup</a>.</li> <li><b><a href="/w/index.php?title=Burnsidovo_lemma&action=edit&redlink=1" class="new" title="Burnsidovo lemma (stránka neexistuje)">Burnsidovo lemma</a></b>: Počet <a href="/w/index.php?title=Orbita_(teorie_grup)&action=edit&redlink=1" class="new" title="Orbita (teorie grup) (stránka neexistuje)">orbit</a> <a href="/wiki/Akce_grupy_na_mno%C5%BEinu" class="mw-redirect" title="Akce grupy na množinu">akce grupy na množinu</a> se rovná průměrnému počtu bodů fixovaných jednotlivými prvky grupy.</li> <li><b><a href="/w/index.php?title=Klasifikace_kone%C4%8Dn%C4%9B_generovan%C3%BDch_abelovsk%C3%BDch_grup&action=edit&redlink=1" class="new" title="Klasifikace konečně generovaných abelovských grup (stránka neexistuje)">Klasifikace konečně generovaných abelovských grup</a></b>: Každá <a href="/wiki/Generov%C3%A1n%C3%AD_grupy" title="Generování grupy">konečně generovaná</a> <a href="/wiki/Abelovsk%C3%A1_grupa" class="mw-redirect" title="Abelovská grupa">abelovská grupa</a> je jednoznačně vyjádřitelná jako <a href="/wiki/Direktn%C3%AD_sou%C4%8Det_grup" class="mw-redirect" title="Direktní součet grup">direktní suma</a> <a href="/wiki/Cyklick%C3%A1_grupa" title="Cyklická grupa">cyklických grup</a> <a href="/wiki/%C5%98%C3%A1d_grupy" class="mw-redirect" title="Řád grupy">řádu</a> nekonečného nebo mocniny <a href="/wiki/Prvo%C4%8D%C3%ADslo" title="Prvočíslo">prvočísla</a>.</li> <li><b><a href="/wiki/Klasifikace_kone%C4%8Dn%C3%BDch_jednoduch%C3%BDch_grup" class="mw-redirect" title="Klasifikace konečných jednoduchých grup">Klasifikace konečných jednoduchých grup</a></b>: Jeden z vrcholných výsledků matematiky <a href="/wiki/20._stolet%C3%AD" title="20. století">20. století</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Odkazy">Odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorie_grup&veaction=edit&section=4" title="Editace sekce: Odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorie_grup&action=edit&section=4" title="Editovat zdrojový kód sekce Odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Související_články"><span id="Souvisej.C3.ADc.C3.AD_.C4.8Dl.C3.A1nky"></span>Související články</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorie_grup&veaction=edit&section=5" title="Editace sekce: Související články" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorie_grup&action=edit&section=5" title="Editovat zdrojový kód sekce Související články"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Grupa" title="Grupa">Grupa</a></li> <li><a href="/wiki/Teorie_t%C4%9Bles" class="mw-redirect" title="Teorie těles">Teorie těles</a></li> <li><a href="/wiki/Teorie_okruh%C5%AF" class="mw-redirect" title="Teorie okruhů">Teorie okruhů</a></li> <li><a href="/wiki/Galoisova_teorie" title="Galoisova teorie">Galoisova teorie</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorie_grup&veaction=edit&section=6" title="Editace sekce: Externí odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorie_grup&action=edit&section=6" title="Editovat zdrojový kód sekce Externí odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="wd"><span class="sisterproject sisterproject-commons"><span class="sisterproject_image"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons"><img alt="Logo Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></span> <span class="sisterproject_text">Obrázky, zvuky či videa k tématu <span class="sisterproject_text_target"><a href="https://commons.wikimedia.org/wiki/Category:Group_theory" class="extiw" title="c:Category:Group theory">teorie grup</a></span> na <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a></span></span></span><i> </i></li></ul> <div class="mw-heading mw-heading3"><h3 id="Literatura">Literatura</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorie_grup&veaction=edit&section=7" title="Editace sekce: Literatura" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorie_grup&action=edit&section=7" title="Editovat zdrojový kód sekce Literatura"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="book" style="font-style:normal;">DRÁPAL, Aleš. <i>Teorie grup – základní aspekty</i>. Praha: Karolinum, 2000. <span style="white-space:nowrap"><a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Speci%C3%A1ln%C3%AD:Zdroje_knih/80-246-0162-1" title="Speciální:Zdroje knih/80-246-0162-1"><span class="ISBN">80-246-0162-1</span></a></span>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/cs.wikipedia.org:templatecitacemonografie&rft.btitle=Teorie+grup+%E2%80%93+z%C3%A1kladn%C3%AD+aspekty&rft.isbn=80-246-0162-1&rft.aulast=Dr%C3%A1pal&rft.aufirst=Ale%C5%A1&rft.place=Praha&rft.pub=Karolinum&rft.date=2000"><span style="display:none"> </span></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r23078045">.mw-parser-output .navbox2{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox2 .navbox2{margin-top:0}.mw-parser-output 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