Alperin-Brauer-Gorenstein-Theorem

Alperin–Brauer–Gorenstein theorem In mathematics, 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).

Notes ^ A 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, das ist, if it is the wreath product of a cyclic 2-group with the symmetric group on 2 Punkte. References Alperin, J. L.; Brauer, R.; Gorenstein, D. (1970), "Finite groups with quasi-dihedral and wreathed Sylow 2-subgroups.", Transaktionen der American Mathematical Society, Amerikanische Mathematische Gesellschaft, 151 (1): 1–261, doi:10.2307/1995627, ISSN 0002-9947, JSTOR 1995627, HERR 0284499 Gorenstein, D. (1968), Finite groups, Harper & Row Publishers, HERR 0231903 Kwon, T.; Lee, K.; Cho, ICH.; Park, S. (1980), "On finite groups with quasidihedral Sylow 2-groups", Journal of the Korean Mathematical Society, 17 (1): 91–97, ISSN 0304-9914, HERR 0593804, ab dem Original archiviert 2011-07-22, abgerufen 2010-07-16 Dieser Artikel über abstrakte Algebra ist ein Stummel. Sie können Wikipedia helfen, indem Sie es erweitern.

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