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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 almost simple group ： ウィキペディア英語版 almost simple group In mathematics, a group is said to be almost simple if it contains a non-abelian simple group and is contained within the automorphism group of that simple group: if it fits between a (non-abelian) simple group and its automorphism group. In symbols, a group ''A'' is almost simple if there is a simple group ''S'' such that $S\; \backslash leq\; A\; \backslash leq\; \backslash operatorname(S).$ == Examples == * Trivially, nonabelian simple groups and the full group of automorphisms are almost simple, but proper examples exist, meaning almost simple groups that are neither simple nor the full automorphism group. * For $n=5$ or $n\; \backslash geq\; 7,$ the symmetric group $S\_n$ is the automorphism group of the simple alternating group $A\_n,$ so $S\_n$ is almost simple in this trivial sense. * For $n=6$ there is a proper example, as $S\_6$ sits properly between the simple $A\_6$ and $\backslash operatorname(A\_6),$ due to the exceptional outer automorphism of $A\_6.$ Two other groups, the Mathieu group $M\_$ and the projective general linear group $\backslash operatorname\_2(9)$ also sit properly between $A\_6$ and $\backslash operatorname(A\_6).$ 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「almost simple group」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.