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

Alperin, J. L.; Brauer, Richard; Gorenstein, Daniel

doi:10.1090/S0002-9947-1970-0284499-5

Finite groups with quasi-dihedral and wreathed Sylow $2$-subgroups.
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Trans. Amer. Math. Soc. 151 (1970), 1-261 Request permission

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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