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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 L-balance theorem ： ウィキペディア英語版 L-balance theorem In mathematical finite group theory, the L-balance theorem was proved by . The letter ''L'' stands for the layer of a group, and "balance" refers to the property discussed below. ==Statement== The L-balance theorem of Gorenstein and Walter states that if ''X'' is a finite group and ''T'' a 2-subgroup of ''X'' then :$L\_(C\_X(T))\; \backslash le\; L\_(X)$ Here ''L''2′(''X'') stands for the 2-layer of a group ''X'', which is the product of all the 2-components of the group, the minimal subnormal subgroups of ''X'' mapping onto components of ''X''/''O''(''X''). A consequence is that if ''a'' and ''b'' are commuting involutions of a group ''G'' then :$L\_(L\_(C\_a)\backslash cap\; C\_b)\; =\; L\_(L\_(C\_b)\backslash cap\; C\_a)$ This is the property called ''L''-balance. More generally similar results are true if the prime 2 is replaced by an prime ''p'', and in this case the condition is called ''L''''p''-balance, but the proof of this requires the classification of finite simple groups (more precisely the Schreier conjecture). 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「L-balance theorem」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.