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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 Zassenhaus lemma ： ウィキペディア英語版 Zassenhaus lemma In mathematics, the butterfly lemma or Zassenhaus lemma, named after Hans Zassenhaus, is a technical result on the lattice of subgroups of a group or the lattice of submodules of a module, or more generally for any modular lattice.〔See Pierce, p. 27, exercise 1.〕 Lemma: Suppose $(G,\; \backslash Omega)$ is a group with operators and $A$ and $C$ are subgroups. Suppose :$B\backslash triangleleft\; A$ and $D\backslash triangleleft\; C$ are stable subgroups. Then, :$(A\backslash cap\; C)B/(A\backslash cap\; D)B$ is isomorphic to $(A\backslash cap\; C)D/(B\backslash cap\; C)D.$ Zassenhaus proved this lemma specifically to give the smoothest proof of the Schreier refinement theorem. The 'butterfly' becomes apparent when trying to draw the Hasse diagram of the various groups involved. Zassenhaus' lemma for groups can be derived from a more general result known as Goursat's theorem stated in a Goursat variety (of which groups are an instance); however the group-specific modular law also needs to be used in the derivation. ==Notes== 〔 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「Zassenhaus 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.