Alperin-Brauer-Gorenstein-Theorem

In Mathematik, 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
{Anzeigestil M_{11}}
. Alperin, Brauer & Gorenstein (1970) proved this in the course of 261 Seiten. 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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Im Mathematik, das Alperin-Brauer-Gorenstein-Theorem characterizes the finite simple groups mit quasidihedral or wreathed^[1] Sylow 2-subgroups. These are isomorphic either to three-dimensional projective special linear groups oder projective special unitary groups over a finite field of odd order, depending on a certain congruence, or to the Mathieu group

{Anzeigestil M_{11}}

$"M_{11}"$ .

Alperin, Brauer & Gorenstein (1970) proved this in the course of 261 Seiten.

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).

Índice

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^ A 2-group is wreathed if it is a nonabelian semidirect product of a maximal subgroup that is a direktes Produkt of two cyclic groups of the same order, das ist, if it is the wreath product of a cyclic 2-group with the symmetric group an 2 Punkte.