A complete classification of solvable factors of almost simple groups
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911106401828864 |
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| author | Feng, Tao Li, Cai Heng Li, Conghui Wang, Lei Xia, Binzhou Zou, Hanlin |
| author_facet | Feng, Tao Li, Cai Heng Li, Conghui Wang, Lei Xia, Binzhou Zou, Hanlin |
| contents | We give an explicit characterization of solvable factors in factorizations of finite classical groups of Lie type. This completes the classification of solvable factors in factorizations of almost simple groups, finishing the program initiated in [Memoirs of the AMS, 279 (2022), no.~1375] and [Advances in Mathematics, 377 (2021), 107499]. In particular, it resolves the final remaining case in the long-standing problem of determining exact factorizations of almost simple groups. As a byproduct, we obtain a new characterization of one-dimensional transitive groups, offering further insights into their group structures. We also apply our classification to describe quasiprimitive permutation groups with a solvable transitive subgroup, leading to an interesting result that these subgroups are ``small''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A complete classification of solvable factors of almost simple groups Feng, Tao Li, Cai Heng Li, Conghui Wang, Lei Xia, Binzhou Zou, Hanlin Group Theory We give an explicit characterization of solvable factors in factorizations of finite classical groups of Lie type. This completes the classification of solvable factors in factorizations of almost simple groups, finishing the program initiated in [Memoirs of the AMS, 279 (2022), no.~1375] and [Advances in Mathematics, 377 (2021), 107499]. In particular, it resolves the final remaining case in the long-standing problem of determining exact factorizations of almost simple groups. As a byproduct, we obtain a new characterization of one-dimensional transitive groups, offering further insights into their group structures. We also apply our classification to describe quasiprimitive permutation groups with a solvable transitive subgroup, leading to an interesting result that these subgroups are ``small''. |
| title | A complete classification of solvable factors of almost simple groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2407.12416 |