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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Goursat's lemma ： ウィキペディア英語版 Goursat's lemma : ''Not to be confused with Goursat's integral lemma from Complex analysis'' Goursat's lemma, named after the French mathematician Édouard Goursat, is an algebraic theorem about subgroups of the direct product of two groups. It can be stated more generally in a Goursat variety (and consequently it also holds in any Maltsev variety), from which one recovers a more general version of Zassenhaus' butterfly lemma and in this form Goursat's theorem also implies the snake lemma. == Groups == Goursat's lemma for groups can be stated as follows. :Let $G$, $G\text{'}$ be groups, and let $H$ be a subgroup of $G\backslash times\; G\text{'}$ such that the two projections $p\_1:\; H\backslash rightarrow\; G$ and $p\_2:\; H\backslash rightarrow\; G\text{'}$ are surjective (i.e., $H$ is a subdirect product of $G$ and $G\text{'}$). Let $N$ be the kernel of $p\_1$ and $N\text{'}$ the kernel of $p\_2$. One can identify $N$ as a normal subgroup of $G$, and $N\text{'}$ as a normal subgroup of $G\text{'}$. Then the image of $H$ in $G/N\backslash times\; G\text{'}/N\text{'}$ is the graph of an isomorphism $G/N\backslash approx\; G\text{'}/N\text{'}$. An immediate consequence of this is that the subdirect product of two groups can be described as a fiber product and vice versa. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Goursat's lemma」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.