In mathematics, the Alperin–Brauer–Gorenstein theorem characterizes the finite simple groups with quasidihedral or wreathedA 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 field of odd order, depending on a certain congruence, or to the Mathieu group . 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 .
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