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In finite group theory, an area of abstract algebra, a strongly embedded subgroup of a finite group ''G'' is a proper subgroup ''H'' of even order such that ''H'' ∩ ''H''''g'' has odd order whenever ''g'' is not in ''H''. The Bender–Suzuki theorem, proved by extending work of , classifies the groups ''G'' with a strongly embedded subgroup ''H''. It states that that either # ''G'' has cyclic or generalized quaternion Sylow 2-subgroups and ''H'' contains the centralizer of an involution # or ''G''/''O''(''G'') has a normal subgroup of odd index isomorphic to one of the simple groups PSL2(''q''), Sz(''q'') or PSU3(''q'') where ''q''≥4 is a power of 2 and ''H'' is ''O''(''G'')N''G''(''S'') for some Sylow 2-subgroup ''S''. revised Suzuki's part of the proof. extended Bender's classification to groups with a proper 2-generated core. ==References== * * * * * 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「Strongly embedded subgroup」の詳細全文を読む スポンサード リンク
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