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</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="Sayt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Abel toparı</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="Basqa tildegi maqalaǵa ótiń. 56 tilde bar" > <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-56" 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">56 til</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Abelse_groep" title="Abelse groep – африкаанс тілі" lang="af" hreflang="af" data-title="Abelse groep" data-language-autonym="Afrikaans" data-language-local-name="африкаанс тілі" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B2%D9%85%D8%B1%D8%A9_%D8%A2%D8%A8%D9%84%D9%8A%D8%A9" title="زمرة آبلية – араб тілі" lang="ar" hreflang="ar" data-title="زمرة آبلية" data-language-autonym="العربية" data-language-local-name="араб тілі" 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/Grupu_abelianu" title="Grupu abelianu – астурия тілі" lang="ast" hreflang="ast" data-title="Grupu abelianu" data-language-autonym="Asturianu" data-language-local-name="астурия тілі" 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/Abel_ortalamalar%C4%B1" title="Abel ortalamaları – әзірбайжан тілі" lang="az" hreflang="az" data-title="Abel ortalamaları" data-language-autonym="Azərbaycanca" data-language-local-name="әзірбайжан тілі" 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%90%D0%B1%D0%B5%D0%BB%D1%8C_%D1%82%D3%A9%D1%80%D0%BA%D3%A9%D0%BC%D3%A9" title="Абель төркөмө – башқұрт тілі" lang="ba" hreflang="ba" data-title="Абель төркөмө" data-language-autonym="Башҡортса" data-language-local-name="башқұрт тілі" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%B1%D0%B5%D0%BB%D0%B5%D0%B2%D0%B0_%D0%B3%D1%80%D1%83%D0%BF%D0%B0" title="Абелева група – беларусь тілі" lang="be" hreflang="be" data-title="Абелева група" data-language-autonym="Беларуская" data-language-local-name="беларусь тілі" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%B1%D0%B5%D0%BB%D0%BE%D0%B2%D0%B0_%D0%B3%D1%80%D1%83%D0%BF%D0%B0" title="Абелова група – болгар тілі" lang="bg" hreflang="bg" data-title="Абелова група" data-language-autonym="Български" data-language-local-name="болгар тілі" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%86%E0%A6%AC%E0%A7%87%E0%A6%B2%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%97%E0%A7%8D%E0%A6%B0%E0%A7%81%E0%A6%AA" title="আবেলীয় গ্রুপ – бенгал тілі" lang="bn" hreflang="bn" data-title="আবেলীয় গ্রুপ" data-language-autonym="বাংলা" data-language-local-name="бенгал тілі" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Grup_abeli%C3%A0" title="Grup abelià – каталан тілі" lang="ca" hreflang="ca" data-title="Grup abelià" data-language-autonym="Català" data-language-local-name="каталан тілі" 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/%DA%AF%D8%B1%D9%88%D9%88%D9%BE%DB%8C_%D8%A6%D8%A7%DA%B5%D9%88%DA%AF%DB%86%DA%95%DB%8C" title="گرووپی ئاڵوگۆڕی – сорани тілі" lang="ckb" hreflang="ckb" data-title="گرووپی ئاڵوگۆڕی" data-language-autonym="کوردی" data-language-local-name="сорани тілі" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Abelova_grupa" title="Abelova grupa – чех тілі" lang="cs" hreflang="cs" data-title="Abelova grupa" data-language-autonym="Čeština" data-language-local-name="чех тілі" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Abelsk_gruppe" title="Abelsk gruppe – дат тілі" lang="da" hreflang="da" data-title="Abelsk gruppe" data-language-autonym="Dansk" data-language-local-name="дат тілі" 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/Abelsche_Gruppe" title="Abelsche Gruppe – неміс тілі" lang="de" hreflang="de" data-title="Abelsche Gruppe" data-language-autonym="Deutsch" data-language-local-name="неміс тілі" 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%91%CE%B2%CE%B5%CE%BB%CE%B9%CE%B1%CE%BD%CE%AE_%CE%BF%CE%BC%CE%AC%CE%B4%CE%B1" title="Αβελιανή ομάδα – грек тілі" lang="el" hreflang="el" data-title="Αβελιανή ομάδα" data-language-autonym="Ελληνικά" data-language-local-name="грек тілі" 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/Abelian_group" title="Abelian group – ағылшын тілі" lang="en" hreflang="en" data-title="Abelian group" data-language-autonym="English" data-language-local-name="ағылшын тілі" 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/Komuta_grupo" title="Komuta grupo – эсперанто тілі" lang="eo" hreflang="eo" data-title="Komuta grupo" data-language-autonym="Esperanto" data-language-local-name="эсперанто тілі" 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/Grupo_abeliano" title="Grupo abeliano – испан тілі" lang="es" hreflang="es" data-title="Grupo abeliano" data-language-autonym="Español" data-language-local-name="испан тілі" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Abeli_r%C3%BChm" title="Abeli rühm – эстон тілі" lang="et" hreflang="et" data-title="Abeli rühm" data-language-autonym="Eesti" data-language-local-name="эстон тілі" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Talde_abeldar" title="Talde abeldar – баск тілі" lang="eu" hreflang="eu" data-title="Talde abeldar" data-language-autonym="Euskara" data-language-local-name="баск тілі" 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/%DA%AF%D8%B1%D9%88%D9%87_%D8%A2%D8%A8%D9%84%DB%8C" title="گروه آبلی – парсы тілі" lang="fa" hreflang="fa" data-title="گروه آبلی" data-language-autonym="فارسی" data-language-local-name="парсы тілі" 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/Abelin_ryhm%C3%A4" title="Abelin ryhmä – фин тілі" lang="fi" hreflang="fi" data-title="Abelin ryhmä" data-language-autonym="Suomi" data-language-local-name="фин тілі" 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/Groupe_ab%C3%A9lien" title="Groupe abélien – француз тілі" lang="fr" hreflang="fr" data-title="Groupe abélien" data-language-autonym="Français" data-language-local-name="француз тілі" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Grupo_abeliano" title="Grupo abeliano – галисия тілі" lang="gl" hreflang="gl" data-title="Grupo abeliano" data-language-autonym="Galego" data-language-local-name="галисия тілі" 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%97%D7%91%D7%95%D7%A8%D7%94_%D7%90%D7%91%D7%9C%D7%99%D7%AA" title="חבורה אבלית – иврит тілі" lang="he" hreflang="he" data-title="חבורה אבלית" data-language-autonym="עברית" data-language-local-name="иврит тілі" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Abelova_grupa" title="Abelova grupa – хорват тілі" lang="hr" hreflang="hr" data-title="Abelova grupa" data-language-autonym="Hrvatski" data-language-local-name="хорват тілі" 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/Abel-csoport" title="Abel-csoport – венгр тілі" lang="hu" hreflang="hu" data-title="Abel-csoport" data-language-autonym="Magyar" data-language-local-name="венгр тілі" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%A2%D5%A5%D5%AC%D5%B5%D5%A1%D5%B6_%D5%AD%D5%B8%D6%82%D5%B4%D5%A2" title="Աբելյան խումբ – армян тілі" lang="hy" hreflang="hy" data-title="Աբելյան խումբ" data-language-autonym="Հայերեն" data-language-local-name="армян тілі" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Gruppo_abelian" title="Gruppo abelian – интерлингва тілі" lang="ia" hreflang="ia" data-title="Gruppo abelian" data-language-autonym="İnterlingua" data-language-local-name="интерлингва тілі" class="interlanguage-link-target"><span>İnterlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Grup_Abelian" title="Grup Abelian – индонезия тілі" lang="id" hreflang="id" data-title="Grup Abelian" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонезия тілі" 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/Gruppo_abeliano" title="Gruppo abeliano – итальян тілі" lang="it" hreflang="it" data-title="Gruppo abeliano" data-language-autonym="İtaliano" data-language-local-name="итальян тілі" class="interlanguage-link-target"><span>İtaliano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A2%E3%83%BC%E3%83%99%E3%83%AB%E7%BE%A4" title="アーベル群 – жапон тілі" lang="ja" hreflang="ja" data-title="アーベル群" data-language-autonym="日本語" data-language-local-name="жапон тілі" 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/%EC%95%84%EB%B2%A8_%EA%B5%B0" title="아벨 군 – корей тілі" lang="ko" hreflang="ko" data-title="아벨 군" data-language-autonym="한국어" data-language-local-name="корей тілі" 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/Caterva_Abeliana" title="Caterva Abeliana – латын тілі" lang="la" hreflang="la" data-title="Caterva Abeliana" data-language-autonym="Latina" data-language-local-name="латын тілі" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B5%8D%E0%B4%B0%E0%B4%AE%E0%B4%97%E0%B5%8D%E0%B4%B0%E0%B5%82%E0%B4%AA%E0%B5%8D%E0%B4%AA%E0%B5%8D" title="ക്രമഗ്രൂപ്പ് – малаялам тілі" lang="ml" hreflang="ml" data-title="ക്രമഗ്രൂപ്പ്" data-language-autonym="മലയാളം" data-language-local-name="малаялам тілі" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kumpulan_Abel" title="Kumpulan Abel – малай тілі" lang="ms" hreflang="ms" data-title="Kumpulan Abel" data-language-autonym="Bahasa Melayu" data-language-local-name="малай тілі" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Abelse_groep" title="Abelse groep – нидерланд тілі" lang="nl" hreflang="nl" data-title="Abelse groep" data-language-autonym="Nederlands" data-language-local-name="нидерланд тілі" 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/Abelsk_gruppe" title="Abelsk gruppe – норвегиялық нюнорск тілі" lang="nn" hreflang="nn" data-title="Abelsk gruppe" data-language-autonym="Norsk nynorsk" data-language-local-name="норвегиялық нюнорск тілі" 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/Abelsk_gruppe" title="Abelsk gruppe – норвегиялық букмол тілі" lang="nb" hreflang="nb" data-title="Abelsk gruppe" data-language-autonym="Norsk bokmål" data-language-local-name="норвегиялық букмол тілі" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Abelan_grupe" title="Abelan grupe – Novial" lang="nov" hreflang="nov" data-title="Abelan grupe" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Grupa_przemienna" title="Grupa przemienna – поляк тілі" lang="pl" hreflang="pl" data-title="Grupa przemienna" data-language-autonym="Polski" data-language-local-name="поляк тілі" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Grupo_abeliano" title="Grupo abeliano – португал тілі" lang="pt" hreflang="pt" data-title="Grupo abeliano" data-language-autonym="Português" data-language-local-name="португал тілі" 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/Grup_abelian" title="Grup abelian – румын тілі" lang="ro" hreflang="ro" data-title="Grup abelian" data-language-autonym="Română" data-language-local-name="румын тілі" 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%90%D0%B1%D0%B5%D0%BB%D0%B5%D0%B2%D0%B0_%D0%B3%D1%80%D1%83%D0%BF%D0%BF%D0%B0" title="Абелева группа – орыс тілі" lang="ru" hreflang="ru" data-title="Абелева группа" data-language-autonym="Русский" data-language-local-name="орыс тілі" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Abelova_grupa" title="Abelova grupa – серб-хорват тілі" lang="sh" hreflang="sh" data-title="Abelova grupa" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="серб-хорват тілі" 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/Abelian_group" title="Abelian group – Simple English" lang="en-simple" hreflang="en-simple" data-title="Abelian group" 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/Abelovsk%C3%A1_grupa" title="Abelovská grupa – словак тілі" lang="sk" hreflang="sk" data-title="Abelovská grupa" data-language-autonym="Slovenčina" data-language-local-name="словак тілі" 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/Abelova_grupa" title="Abelova grupa – словен тілі" lang="sl" hreflang="sl" data-title="Abelova grupa" data-language-autonym="Slovenščina" data-language-local-name="словен тілі" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%B1%D0%B5%D0%BB%D0%BE%D0%B2%D0%B0_%D0%B3%D1%80%D1%83%D0%BF%D0%B0" title="Абелова група – серб тілі" lang="sr" hreflang="sr" data-title="Абелова група" data-language-autonym="Српски / srpski" data-language-local-name="серб тілі" 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/Abelsk_grupp" title="Abelsk grupp – швед тілі" lang="sv" hreflang="sv" data-title="Abelsk grupp" data-language-autonym="Svenska" data-language-local-name="швед тілі" 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%AA%E0%AE%B0%E0%AE%BF%E0%AE%AE%E0%AE%BE%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AF%81%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AF%81%E0%AE%B2%E0%AE%AE%E0%AF%8D" title="பரிமாற்றுக் குலம் – тамил тілі" lang="ta" hreflang="ta" data-title="பரிமாற்றுக் குலம்" data-language-autonym="தமிழ்" data-language-local-name="тамил тілі" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Abel_grubu" title="Abel grubu – түрік тілі" lang="tr" hreflang="tr" data-title="Abel grubu" data-language-autonym="Türkçe" data-language-local-name="түрік тілі" 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%90%D0%B1%D0%B5%D0%BB%D0%B5%D0%B2%D0%B0_%D0%B3%D1%80%D1%83%D0%BF%D0%B0" title="Абелева група – украин тілі" lang="uk" hreflang="uk" data-title="Абелева група" data-language-autonym="Українська" data-language-local-name="украин тілі" 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/Nh%C3%B3m_giao_ho%C3%A1n" title="Nhóm giao hoán – вьетнам тілі" lang="vi" hreflang="vi" data-title="Nhóm giao hoán" data-language-autonym="Tiếng Việt" data-language-local-name="вьетнам тілі" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%98%BF%E8%B4%9D%E5%B0%94%E7%BE%A4" title="阿贝尔群 – қытай тілі" lang="zh" hreflang="zh" data-title="阿贝尔群" data-language-autonym="中文" data-language-local-name="қытай тілі" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E4%BA%A4%E6%8F%9B%E7%BE%A4" title="交換群 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="交換群" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%98%BF%E8%B2%9D%E7%88%BE%E7%BE%A3" title="阿貝爾羣 – кантон тілі" lang="yue" hreflang="yue" data-title="阿貝爾羣" data-language-autonym="粵語" data-language-local-name="кантон тілі" 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/Q181296#sitelinks-wikipedia" title="Tiller aralıq siltemelerdi redaktorlaw" class="wbc-editpage">Siltemelerdi redaktorlaw</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Atamalar kópligi"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Abel_topar%C4%B1" title="Maǵlıwmat betin kóriw [c]" accesskey="c"><span>Maqala</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talq%C4%B1law:Abel_topar%C4%B1" rel="discussion" title="Maǵlıwmat beti haqqında talqılaw [t]" accesskey="t"><span>Talqılaw</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Til variantın ózgertiw" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Qaraqalpaqsha</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Kórinisler"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Abel_topar%C4%B1"><span>Tanısıp shıǵıw</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Abel_topar%C4%B1&veaction=edit" title="Bul betti ózgertiw [v]" accesskey="v"><span>Redaktorlaw</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Abel_topar%C4%B1&action=edit" title="Bul bettiń derek kodın ózgertiw [e]" accesskey="e"><span>Derekti redaktorlaw</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Abel_topar%C4%B1&action=history" title="Bettiń aldınǵı ózgerisleri [h]" accesskey="h"><span>Tariyxın kóriw</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Bet ásbapları"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Ásbaplar" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Ásbaplar</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Ásbaplar</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">qaptal panelge kóshiriw</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">jasırıw</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Kóbirek parametrler" > <div class="vector-menu-heading"> Háreketler </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Abel_topar%C4%B1"><span>Tanısıp shıǵıw</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Abel_topar%C4%B1&veaction=edit" title="Bul betti ózgertiw [v]" accesskey="v"><span>Redaktorlaw</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Abel_topar%C4%B1&action=edit" title="Bul bettiń derek kodın ózgertiw [e]" accesskey="e"><span>Derekti redaktorlaw</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Abel_topar%C4%B1&action=history"><span>Tariyxın kóriw</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Ulıwma </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Arnawl%C4%B1:Siltelgen_betler/Abel_topar%C4%B1" title="Usı betke siltelgen barlıq betler dizimi [j]" accesskey="j"><span>Siltelgen betler</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Arnawl%C4%B1:Baylan%C4%B1sl%C4%B1_aq%C4%B1r%C7%B5%C4%B1_%C3%B3zgerisler/Abel_topar%C4%B1" rel="nofollow" title="Bul betten siltengen betlerdegi aqırǵı ózgerisler [k]" accesskey="k"><span>Baylanıslı ózgerisler</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=kaa" title="Fayllar júklew [u]" accesskey="u"><span>Fayl júklew</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Arnawl%C4%B1:Arnawl%C4%B1_betler" title="Barlıq arnawlı betler dizimi [q]" accesskey="q"><span>Arnawlı betler</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Abel_topar%C4%B1&oldid=51998" title="Bul bettegi usı nusqasınıń turaqlı siltemesi"><span>Turaqlı silteme</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Abel_topar%C4%B1&action=info" title="Ashıq turǵan bet haqqında kóbirek maǵlıwmat"><span>Bet haqqında maǵlıwmat</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Arnawl%C4%B1:CiteThisPage&page=Abel_topar%C4%B1&id=51998&wpFormIdentifier=titleform" title="Bul betti kóshirip alǵanda qalay citata keltiriw haqqında maǵlıwmat"><span>Betke silteme jaratıw</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Arnawl%C4%B1:UrlShortener&url=https%3A%2F%2Fkaa.wikipedia.org%2Fwiki%2FAbel_topar%25C4%25B1"><span>Qısqartılǵan URL alıw</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Arnawl%C4%B1:QrCode&url=https%3A%2F%2Fkaa.wikipedia.org%2Fwiki%2FAbel_topar%25C4%25B1"><span>QR kod júklep alıw</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Basıp shıǵarıw/eksport </div> <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=Arnawl%C4%B1:Book&bookcmd=book_creator&referer=Abel+topar%C4%B1"><span>Kitap jaratıw</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Arnawl%C4%B1:DownloadAsPdf&page=Abel_topar%C4%B1&action=show-download-screen"><span>PDF túrinde júklep alıw</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Abel_topar%C4%B1&printable=yes" title="Bul bettiń baspa nusqası [p]" accesskey="p"><span>Baspa nusqası</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Basqa joybarlarda </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Abelian_groups" hreflang="en"><span>Wikiqoyma</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/Q181296" title="Baylanısqan Wikimaǵlıwmat bazası elementine silteme [g]" accesskey="g"><span>Wikimaǵlıwmat elementi</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Bet ásbapları"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Kórinis"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Kórinis</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">qaptal panelge kóshiriw</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">jasırıw</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Wikipedia, erkin enciklopediya</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="kaa" dir="ltr"><p><b>Abel gruppası</b> (yamasa kommutativ gruppa; Abelian group; Абелева группа) - dep <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 {A} ,*>}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo><</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> </mrow> <mo>,</mo> <mo>∗</mo> <mo>></mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle <\mathbb {A} ,*>}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1079f20a084eea3ce8cab84cb9859d7c5a4c40a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.781ex; height:2.509ex;" alt="{\displaystyle <\mathbb {A} ,*>}"></span> gruppada berilgen <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 *}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle *}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e9972f426d9e07855984f73ee195a21dbc21755" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle *}"></span> <a href="/wiki/Algebra" title="Algebra">algebralıq</a> ámeli kommutativ bolǵanda, yaǵnıy ıqtıyarıy <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 a,b\in \mathbb {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a,b\in \mathbb {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ff757c93aa94393e8f39bc34c2bc29e35f96d71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.78ex; height:2.509ex;" alt="{\displaystyle a,b\in \mathbb {A} }"></span> ushın <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 a*b=b*a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>∗</mo> <mi>b</mi> <mo>=</mo> <mi>b</mi> <mo>∗</mo> 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