Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Li, Tianze, Zeng, Yu
Institutions: Huaqiao University, Suzhou University of Technology
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7589008706
OpenAlex ID: W7221761483