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arXiv · 2011.13016

Finite $2$-groups with exactly three automorphism orbits

Alexander Bors·Stephen P. Glasby
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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.

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Alexander Bors, Stephen P. Glasby. 2020-11-25. Finite $2$-groups with exactly three automorphism orbits. https://arxiv.org/abs/2011.13016

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