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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Finite groups with quasi-dihedral and wreathed Sylow $ 2$-subgroups.


Authors: J. L. Alperin, Richard Brauer and Daniel Gorenstein
Journal: Trans. Amer. Math. Soc. 151 (1970), 1-261
MSC: Primary 20.27
MathSciNet review: 0284499
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Abstract: The primary purpose of this paper is to give a complete classification of all finite simple groups with quasi-dihedral Sylow 2-subgroups. We shall prove that any such group must be isomorphic to one of the groups $ {L_3}(q)$ with $ q \equiv - 1 \pmod 4,{U_3}(q)$ with $ q \equiv 1 \pmod 4$, or $ {M_{11}}$. We shall also carry out a major portion of the corresponding classification of simple groups with Sylow 2-subgroups isomorphic to the wreath product of $ {Z_{{2^n}}}$ and $ {Z_2},n \geqq 2$.


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DOI: https://doi.org/10.1090/S0002-9947-1970-0284499-5
Keywords: Quasi-dihedral, wreathed, Q-group, D-group, QD-group, regular group
Article copyright: © Copyright 1970 American Mathematical Society