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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.01725 |
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| _version_ | 1866910928539222016 |
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| author | Li, Cai Heng Zhu, Yan Zhou |
| author_facet | Li, Cai Heng Zhu, Yan Zhou |
| contents | A complete classification is given of finite groups whose elements are partitioned into three orbits by the automorphism groups, solving the long-standing classification problem initiated by G. Higman in 1963. As a consequence, a classification is obtained for finite permutation groups of rank $3$ which are holomorphs of groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The finite groups with three automorphism orbits Li, Cai Heng Zhu, Yan Zhou Group Theory A complete classification is given of finite groups whose elements are partitioned into three orbits by the automorphism groups, solving the long-standing classification problem initiated by G. Higman in 1963. As a consequence, a classification is obtained for finite permutation groups of rank $3$ which are holomorphs of groups. |
| title | The finite groups with three automorphism orbits |
| topic | Group Theory |
| url | https://arxiv.org/abs/2403.01725 |