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Sylow $2$-Subgroups of Finite Groups with a Single Conjugacy Class of Involutions
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, gener
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