# Théorème d'Alperin – Brauer – Gorenstein

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

# Théorème d'Alperin – Brauer – Gorenstein

Dans mathématiques, la Théorème d'Alperin – Brauer – Gorenstein characterizes the finite simple groups avec 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

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.

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

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).

Indice

## Remarques[]

1. ^ A 2-group is wreathed if it is a nonabelian semidirect product of a maximal subgroup that is a produit direct of two cyclic groups of the same order, C'est, if it is the wreath product of a cyclic 2-group with the symmetric group sur 2 points.

## Références[]

• Alperin, J. L.Brauer, R.Gorenstein, ré. (1970), "Finite groups with quasi-dihedral and wreathed Sylow 2-subgroups.", Transactions de l'American Mathematical Society, Société mathématique américaine, 151 (1): 1–261, est ce que je:10.2307/1995627, ISSN 0002-9947, JSTOR 1995627, M 0284499

• Gorenstein, ré. (1968), Finite groups, harpiste & Row Publishers, M 0231903
• Kwon, T; Lee, K; Cho, JE.; Park, S. (1980), "On finite groups with quasidihedral Sylow 2-groups", Journal of the Korean Mathematical Society, 17 (1): 91–97, ISSN 0304-9914, M 0593804, archived from the original sur 2011-07-22, récupéré 2010-07-16

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