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In mathematical finite group theory, a block, sometimes called Aschbacher block, is a subgroup giving an obstruction to Thompson factorization and pushing up. Blocks were introduced by Michael Aschbacher. ==Definition== A group ''L'' is called short if it has the following properties : #''L'' has no subgroup of index 2 #The generalized Fitting subgroup ''F'' *(''L'') is a 2-group ''O''2(''L'') #The subgroup ''U'' = (''L'' ) is an elementary abelian 2-group in the center of ''O''2(''L'') #''L''/''O''2(''L'') is quasisimple or of order 3 #''L'' acts irreducibly on ''U''/''C''''U''(''L'') An example of a short group is the semidirect product of a quasisimple group with an irreducible module over the 2-element field F2 A block of a group ''G'' is a short subnormal subgroup. 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「Aschbacher block」の詳細全文を読む スポンサード リンク
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