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[o]" accesskey="o" class=""><span>로그인</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="더 많은 옵션" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="개인 도구" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">개인 도구</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="사용자 메뉴" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=ko.wikipedia.org&uselang=ko"><span>기부</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EA%B3%84%EC%A0%95%EB%A7%8C%EB%93%A4%EA%B8%B0&returnto=%EA%B0%80%EB%B2%95%EA%B5%B0" title="계정을 만들고 로그인하는 것이 좋습니다. 하지만 필수는 아닙니다"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>계정 만들기</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EB%A1%9C%EA%B7%B8%EC%9D%B8&returnto=%EA%B0%80%EB%B2%95%EA%B5%B0" title="위키백과에 로그인하면 여러가지 편리한 기능을 사용할 수 있습니다. 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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="사이트"> <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="목차" 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">목차</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">숨기기</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">처음 위치</div> </a> </li> <li id="toc-군" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#군"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>군</span> </div> </a> <ul id="toc-군-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-승법군" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#승법군"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>승법군</span> </div> </a> <ul id="toc-승법군-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-같이_보기" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#같이_보기"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>같이 보기</span> </div> </a> <ul id="toc-같이_보기-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-각주" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#각주"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>각주</span> </div> </a> <ul id="toc-각주-sublist" class="vector-toc-list"> </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="목차" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="목차" > <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="목차 토글" > <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">목차 토글</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">가법군</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="다른 언어로 문서를 방문합니다. 8개 언어로 읽을 수 있습니다" > <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-8" 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">8개 언어</span> </label> <div class="vector-dropdown-content"> <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/%D8%B2%D9%85%D8%B1%D8%A9_%D8%AC%D9%85%D8%B9%D9%8A%D8%A9" title="زمرة جمعية – 아랍어" lang="ar" hreflang="ar" data-title="زمرة جمعية" data-language-autonym="العربية" data-language-local-name="아랍어" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Additive_group" title="Additive group – 영어" lang="en" hreflang="en" data-title="Additive group" data-language-autonym="English" data-language-local-name="영어" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Grupo_aditivo" title="Grupo aditivo – 스페인어" lang="es" hreflang="es" data-title="Grupo aditivo" data-language-autonym="Español" data-language-local-name="스페인어" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Grup_aditif" title="Grup aditif – 인도네시아어" lang="id" hreflang="id" data-title="Grup aditif" data-language-autonym="Bahasa Indonesia" data-language-local-name="인도네시아어" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8A%A0%E6%B3%95%E7%BE%A4" title="加法群 – 일본어" lang="ja" hreflang="ja" data-title="加法群" data-language-autonym="日本語" data-language-local-name="일본어" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Grupa_addytywna" title="Grupa addytywna – 폴란드어" lang="pl" hreflang="pl" data-title="Grupa addytywna" data-language-autonym="Polski" data-language-local-name="폴란드어" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru badge-Q70894304 mw-list-item" title=""><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%B4%D0%B4%D0%B8%D1%82%D0%B8%D0%B2%D0%BD%D0%B0%D1%8F_%D0%B3%D1%80%D1%83%D0%BF%D0%BF%D0%B0" title="Аддитивная группа – 러시아어" lang="ru" hreflang="ru" data-title="Аддитивная 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<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="보기"> <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/%EA%B0%80%EB%B2%95%EA%B5%B0"><span>읽기</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%EA%B0%80%EB%B2%95%EA%B5%B0&action=edit" title="이 문서의 원본 코드를 편집 [e]" accesskey="e"><span>편집</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%EA%B0%80%EB%B2%95%EA%B5%B0&action=history" title="이 문서의 과거 편집 내역입니다. 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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">도구</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">숨기기</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="더 많은 옵션" > <div class="vector-menu-heading"> 동작 </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 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href="/wiki/%ED%8A%B9%EC%88%98:%EB%A7%81%ED%81%AC%EC%B5%9C%EA%B7%BC%EB%B0%94%EB%80%9C/%EA%B0%80%EB%B2%95%EA%B5%B0" rel="nofollow" title="이 문서에서 링크한 문서의 최근 바뀜 [k]" accesskey="k"><span>가리키는 글의 최근 바뀜</span></a></li><li id="t-upload" class="mw-list-item"><a href="//ko.wikipedia.org/wiki/위키백과:파일_올리기" title="파일 올리기 [u]" accesskey="u"><span>파일 올리기</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%EA%B0%80%EB%B2%95%EA%B5%B0&oldid=37854162" title="이 문서의 이 판에 대한 고유 링크"><span>고유 링크</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%EA%B0%80%EB%B2%95%EA%B5%B0&action=info" title="이 문서에 대한 자세한 정보"><span>문서 정보</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EC%9D%B4%EB%AC%B8%EC%84%9C%EC%9D%B8%EC%9A%A9&page=%EA%B0%80%EB%B2%95%EA%B5%B0&id=37854162&wpFormIdentifier=titleform" title="이 문서를 인용하는 방법에 대한 정보"><span>이 문서 인용하기</span></a></li><li id="t-urlshortener" class="mw-list-item"><a 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class="vector-page-tools-landmark" aria-label="페이지 도구"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="보이기"> <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">보이기</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">숨기기</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">위키백과, 우리 모두의 백과사전.</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="ko" dir="ltr"><p><span class="nowrap"></span> <b>가법군</b>(Additive group,加法群) 또는 덧셈군은 수학에서 <a href="/wiki/%EC%9D%B4%ED%95%AD_%EC%97%B0%EC%82%B0" class="mw-redirect" title="이항 연산">이항 연산</a> <a href="/wiki/%EB%8D%A7%EC%85%88" title="덧셈">덧셈</a>에 대하여 닫혀 있고, <a href="/wiki/%EA%B2%B0%ED%95%A9_%EB%B2%95%EC%B9%99" class="mw-redirect" title="결합 법칙">결합 법칙</a>과 <a href="/wiki/%EA%B5%90%ED%99%98_%EB%B2%95%EC%B9%99" class="mw-redirect" title="교환 법칙">교환 법칙</a>이 성립하는 <a href="/wiki/%EA%B5%B0_(%EC%88%98%ED%95%99)" title="군 (수학)">군</a>이다. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="군"><span id=".EA.B5.B0"></span>군</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EA%B0%80%EB%B2%95%EA%B5%B0&action=edit&section=1" title="부분 편집: 군"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>한편 <a href="/wiki/%EA%B5%B0_(%EC%88%98%ED%95%99)" title="군 (수학)">군</a>(群)은 하나의 연산에 대하여 닫혀 있는 집합에서 <a href="/wiki/%EA%B2%B0%ED%95%A9_%EB%B2%95%EC%B9%99" class="mw-redirect" title="결합 법칙">결합 법칙</a>이 성립하고 <a href="/wiki/%ED%95%AD%EB%93%B1%EC%9B%90" title="항등원">항등원</a>(단위원)과 <a href="/wiki/%EC%97%AD%EC%9B%90" title="역원">역원</a>이 있는 집합이다. 예를 들어, 정수 전체의 집합에서는 임의의 두 원소를 더하여 얻은 결과도 그 집합에 포함되어 있으므로, 정수 전체의 집합은 덧셈에 대하여 군이 된다. </p> <div class="mw-heading mw-heading2"><h2 id="승법군"><span id=".EC.8A.B9.EB.B2.95.EA.B5.B0"></span>승법군</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EA%B0%80%EB%B2%95%EA%B5%B0&action=edit&section=2" title="부분 편집: 승법군"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>가법군에서 연산이 <a href="/wiki/%EA%B3%B1%EC%85%88" title="곱셈">승법</a>(곱셈)인 경우는 <a href="/w/index.php?title=%EC%8A%B9%EB%B2%95%EA%B5%B0&action=edit&redlink=1" class="new" title="승법군 (없는 문서)">승법군</a>(乘法群,Multiplicative group)이 된다. 군(G)은 가법군과 승법군을 포함한다. 한편 이러한 군에 교환법칙을 정의함으로써 <a href="/wiki/%EA%B0%80%ED%99%98%EA%B5%B0" class="mw-redirect" title="가환군">가환군</a>(또는 아벨군)을 얻을수있다. G가 유한한 원소의 집합인 경우는 유한군이며, 무한한 경우 무한군이 된다. </p> <div class="mw-heading mw-heading2"><h2 id="같이_보기"><span id=".EA.B0.99.EC.9D.B4_.EB.B3.B4.EA.B8.B0"></span>같이 보기</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EA%B0%80%EB%B2%95%EA%B5%B0&action=edit&section=3" title="부분 편집: 같이 보기"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%EC%B9%98%ED%99%98%EA%B5%B0" class="mw-redirect" title="치환군">치환군</a></li> <li><a href="/wiki/%EB%B6%80%EB%B6%84%EA%B5%B0" title="부분군">부분군</a></li> <li><a href="/wiki/%EC%88%9C%ED%99%98%EA%B5%B0" title="순환군">순환군</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="각주"><span id=".EA.B0.81.EC.A3.BC"></span>각주</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EA%B0%80%EB%B2%95%EA%B5%B0&action=edit&section=4" title="부분 편집: 각주"><span>편집</span></a><span 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