Sylow 2-Subgroups of Finite Groups with a Single Conjugacy Class of Involutions
Tianze Li, Yu Zeng
Abstract
We solve Brauer's Problem 33 by determining the finite 2-groups that occur as Sylow 2-subgroups of finite groups with a single conjugacy class of involutions. Besides the Sylow 2-subgroups arising from the relevant non-abelian simple groups in Table 1, these are precisely the homocyclic, generalized quaternion, and Suzuki 2-groups. The classification of finite simple groups is used in this paper.
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