On finite groups in which some maximal invariant subgroups have indices a prime or the square of a prime
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929657354387456 |
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| author | Shi, Jiangtao Tian, Yunfeng |
| author_facet | Shi, Jiangtao Tian, Yunfeng |
| contents | Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms, we first prove some results on the solvability of finite groups in which some maximal $A$-invariant subgroups have indices a prime or the square of a prime. Our results generalize Hall's theorem and some other known results. Moreover, we obtain a complete characterization of finite groups in which every non-nilpotent maximal $A$-invariant subgroup that contains the normalizer of some $A$-invariant Sylow subgroup has index a prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On finite groups in which some maximal invariant subgroups have indices a prime or the square of a prime Shi, Jiangtao Tian, Yunfeng Group Theory 20D10, 20D20 Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms, we first prove some results on the solvability of finite groups in which some maximal $A$-invariant subgroups have indices a prime or the square of a prime. Our results generalize Hall's theorem and some other known results. Moreover, we obtain a complete characterization of finite groups in which every non-nilpotent maximal $A$-invariant subgroup that contains the normalizer of some $A$-invariant Sylow subgroup has index a prime. |
| title | On finite groups in which some maximal invariant subgroups have indices a prime or the square of a prime |
| topic | Group Theory 20D10, 20D20 |
| url | https://arxiv.org/abs/2501.01735 |