Classifying finite groups G with three Aut(G)-orbits
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915159956520960 |
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| author | Glasby, Stephen P. |
| author_facet | Glasby, Stephen P. |
| contents | We give a complete and irredundant list of the finite groups $G$ for which Aut$(G)$, acting naturally on $G$, has precisely $3$ orbits. There are 7 infinite families: one abelian, one non-nilpotent, three families of non-abelian $2$-groups and two families of non-abelian $p$-groups with $p$ odd. The non-abelian $2$-group examples were first classified by Bors and Glasby in 2020 and non-abelian $p$-group examples with $p$ odd were classified independently by Li and Zhu, and by the author, in March 2024. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11273 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classifying finite groups G with three Aut(G)-orbits Glasby, Stephen P. Group Theory 20D45, 20D15 20B10 We give a complete and irredundant list of the finite groups $G$ for which Aut$(G)$, acting naturally on $G$, has precisely $3$ orbits. There are 7 infinite families: one abelian, one non-nilpotent, three families of non-abelian $2$-groups and two families of non-abelian $p$-groups with $p$ odd. The non-abelian $2$-group examples were first classified by Bors and Glasby in 2020 and non-abelian $p$-group examples with $p$ odd were classified independently by Li and Zhu, and by the author, in March 2024. |
| title | Classifying finite groups G with three Aut(G)-orbits |
| topic | Group Theory 20D45, 20D15 20B10 |
| url | https://arxiv.org/abs/2411.11273 |