Finite $2$-groups with exactly three automorphism orbits

Alexander Bors; Stephen P. Glasby

Finite $2$-groups with exactly three automorphism orbits

Group Theory 2025-01-29 v3

Authors: Alexander Bors , Stephen P. Glasby

Abstract

We give a complete classification of the finite $2$ -groups $G$ for which the automorphism group $\operatorname{Aut}(G)$ acting naturally on $G$ has three orbits. There are two infinite families and one additional group, of order $2^9$ . All of them are Suzuki $2$ -groups, and they appear in an earlier classification of Dornhoff.

Keywords

automorphism groups finite group theory group theory

Cite

@article{arxiv.2011.13016,
  title  = {Finite $2$-groups with exactly three automorphism orbits},
  author = {Alexander Bors and Stephen P. Glasby},
  journal= {arXiv preprint arXiv:2011.13016},
  year   = {2025}
}

Comments

18 pages

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