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Walter theorem : ウィキペディア英語版 | Walter theorem In mathematics, the Walter theorem, proved by , describes the finite groups whose Sylow 2-subgroup is abelian. used Bender's method to give a simpler proof. ==Statement== Walter's theorem states that if ''G'' is a finite group whose 2-sylow subgroups are abelian, then ''G''/''O''(''G'') has a normal subgroup of odd index that is a product of groups each of which is a 2-group or one of the simple groups PSL2(''q'') for ''q'' = 2''n'' or ''q'' = 3 or 5 mod 8, or the Janko group J1, or Ree groups 2''G''2(32''n''+1). The original statement of Walter's theorem did not quite identify the Ree groups, but only stated that the corresponding groups have a similar subgroup structure as Ree groups. and later showed that they are all Ree groups, and gave a unified exposition of this result.
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「Walter theorem」の詳細全文を読む
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