Finite $2$-groups with exactly three automorphism orbits
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866915124374142976 |
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| author | Bors, Alexander Glasby, Stephen P. |
| author_facet | Bors, Alexander Glasby, Stephen P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_13016 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Finite $2$-groups with exactly three automorphism orbits Bors, Alexander Glasby, Stephen P. Group Theory Primary: 20D15, 20D45. Secondary: 12E20, 20B10 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. |
| title | Finite $2$-groups with exactly three automorphism orbits |
| topic | Group Theory Primary: 20D15, 20D45. Secondary: 12E20, 20B10 |
| url | https://arxiv.org/abs/2011.13016 |