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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2412.03168 |
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| _version_ | 1866916816383639552 |
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| author | Li, Cai Heng Yi, Hanyue Zhu, Yan Zhou |
| author_facet | Li, Cai Heng Yi, Hanyue Zhu, Yan Zhou |
| contents | A transitive permutation group is said to be semiprimitive if each of its normal subgroups is either semiregular or transitive.The class of semiprimitive groups properly contains primitive groups, quasiprimitive groups and innately transitive groups.The latter three classes of groups of rank $3$ have been classified, forming significant progresses on the long-standing problem of classifying permutation groups of rank $3$.In this paper, a complete classification is given of finite semiprimitive groups of rank $3$ that are not innately transitive, examples of which are certain Schur coverings of certain almost simple $2$-transitive groups, and three exceptional small groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03168 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite semiprimitive permutation groups of rank $3$ Li, Cai Heng Yi, Hanyue Zhu, Yan Zhou Group Theory 20B05 A transitive permutation group is said to be semiprimitive if each of its normal subgroups is either semiregular or transitive.The class of semiprimitive groups properly contains primitive groups, quasiprimitive groups and innately transitive groups.The latter three classes of groups of rank $3$ have been classified, forming significant progresses on the long-standing problem of classifying permutation groups of rank $3$.In this paper, a complete classification is given of finite semiprimitive groups of rank $3$ that are not innately transitive, examples of which are certain Schur coverings of certain almost simple $2$-transitive groups, and three exceptional small groups. |
| title | Finite semiprimitive permutation groups of rank $3$ |
| topic | Group Theory 20B05 |
| url | https://arxiv.org/abs/2412.03168 |