# 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
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. 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

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

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.

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).

Índice

## Notas[]

1. ^ 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.

## Referências[]

• alperin, J. eu.Brauer, R.Gorenstein, D. (1970), "Finite groups with quasi-dihedral and wreathed Sylow 2-subgroups.", Transações da American Mathematical Society, Sociedade Americana de Matemática, 151 (1): 1-261, doi:10.2307/1995627, ISSN 0002-9947, JSTOR 1995627, SENHOR 0284499

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

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