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Alperin–Brauer–Gorenstein theorem : ウィキペディア英語版
Alperin–Brauer–Gorenstein theorem
In mathematics, the Alperin–Brauer–Gorenstein theorem characterizes the finite simple groups with quasidihedral or wreathed〔A 2-group is wreathed if it is a nonabelian semidirect product of a maximal subgroup that is a direct product of two cyclic groups of the same order, that is, if it is the wreath product of a cyclic 2-group with the symmetric group on 2 points.〕 Sylow 2-subgroups. These are isomorphic either to three-dimensional projective special linear groups or projective special unitary groups over a finite fields of odd order, depending on a certain congruence, or to the Mathieu group M_. proved this in the course of 261 pages. The subdivision by 2-fusion is sketched there, given as an exercise in , and presented in some detail in .
==Notes==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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