Alperin–Brauer–Gorenstein theorem

Na matemática, the Alperin–Brauer–Gorenstein theorem characterizes the finite simple groups with quasidihedral or wreathed[1] 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
{estilo de exibição M_{11}}
. alperin, Brauer & Gorenstein (1970) proved this in the course of 261 Páginas. The subdivision by 2-fusion is sketched there, given as an exercise in Gorenstein (1968, CH. 7), and presented in some detail in Kwon et al. (1980).

Alperin–Brauer–Gorenstein theorem

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Dentro matemática, a Alperin–Brauer–Gorenstein theorem characterizes the finite simple groups com quasidihedral or wreathed^[1] Sylow 2-subgroups. These are isomorphic either to three-dimensional projective special linear groups ou projective special unitary groups over a finite field of odd order, depending on a certain congruence, or to the Mathieu group

{estilo de exibição M_{11}}

$"M_{11}"$ .

alperin, Brauer & Gorenstein (1970) proved this in the course of 261 Páginas.

The subdivision by 2-fusion is sketched there, given as an exercise in Gorenstein (1968, CH. 7), and presented in some detail in Kwon et al. (1980).

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^ A 2-group is wreathed if it is a nonabelian semidirect product of a maximal subgroup that is a produto direto of two cyclic groups of the same order, isso é, if it is the wreath product of a cyclic 2-group with the symmetric group sobre 2 pontos.