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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 Isoclinism of groups ： ウィキペディア英語版 Isoclinism of groups In mathematics, specifically group theory, isoclinism is an equivalence relation on groups which generalizes isomorphism. Isoclinism was introduced by to help classify and understand p-groups, although it is applicable to all groups. Isoclinism also has consequences for the Schur multiplier and the associated aspects of character theory, as described in and . The word "isoclinism" comes from the Greek ισοκλινης meaning equal slope. Some textbooks discussing isoclinism include and and . ==Definition== The isoclinism class of a group ''G'' is determined by the groups ''G''/''Z''(''G'') and ''G''′ (the commutator subgroup) and the commutator map from ''G''/''Z''(''G'') × ''G''/''Z''(''G'') to ''G''′ (taking ''a'', ''b'' to ''aba−1b−1''). In other words, two groups ''G''1 and ''G''2 are isoclinic if there are isomorphisms from ''G''1/''Z''(''G''1) to ''G''2/''Z''(''G''2) and from ''G''1′ to ''G''2′ commuting with the commutator map. 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「Isoclinism of groups」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.