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In mathematical finite group theory, a p-group of symplectic type is a ''p''-group such that all characteristic abelian subgroups are cyclic. According to , the ''p''-groups of symplectic type were classified by P. Hall in unpublished lecture notes, who showed that they are all a central product of an extraspecial group with a group that is cyclic, dihedral, quasidihedral, or quaternion. gives a proof of this result. The width ''n'' of a group ''G'' of symplectic type is the largest integer ''n'' such that the group contains an extraspecial subgroup ''H'' of order ''p''1+2''n'' such that ''G'' = ''H''.''C''''G''(''H''), or 0 if ''G'' contains no such subgroup. Groups of symplectic type appear in centralizers of involutions of groups of GF(2)-type. ==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「group of symplectic type」の詳細全文を読む スポンサード リンク
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