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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 Superperfect group ： ウィキペディア英語版 Superperfect group In mathematics, in the realm of group theory, a group is said to be superperfect when its first two homology groups are trivial: ''H''1(''G'', Z) = ''H''2(''G'', Z) = 0. This is stronger than a perfect group, which is one whose first homology group vanishes. In more classical terms, a superperfect group is one whose abelianization and Schur multiplier both vanish; abelianization equals the first homology, while the Schur multiplier equals the second homology. == Definition == The first homology group of a group is the abelianization of the group itself, since the homology of a group ''G'' is the homology of any Eilenberg-MacLane space of type ''K''(''G'', 1); the fundamental group of a ''K''(''G'', 1) is ''G'', and the first homology of ''K''(''G'', 1) is then abelianization of its fundamental group. Thus, if a group is superperfect, then it is perfect. A finite perfect group is superperfect if and only if it is its own universal central extension (UCE), as the second homology group of a perfect group parametrizes central extensions. 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「Superperfect 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.