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PreprintCC BY 4.0arXiv

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

  • Tianze Li
  • Yu Zeng
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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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Cite

BibTeXRIS
BibTeX
@misc{li2026sylow,
  title = {{Sylow $2$-Subgroups of Finite Groups with a Single Conjugacy Class of Involutions}},
  author = {Tianze Li and Yu Zeng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14689},
  eprint = {2610.14689},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14689},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Sylow $2$-Subgroups of Finite Groups with a Single Conjugacy Class of Involutions
AU  - Tianze Li
AU  - Yu Zeng
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.14689
UR  - https://arxiv.org/abs/2610.14689
AB  - 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.
ER  -