Finite groups in which some particular non-nilpotent maximal invariant subgroups have indices a prime-power
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915141507874816 |
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| author | Shi, Jiangtao Shan, Mengjiao Xu, Fanjie |
| author_facet | Shi, Jiangtao Shan, Mengjiao Xu, Fanjie |
| contents | Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms, assume that $G$ has a maximal $A$-invariant subgroup $M$ that is a direct product of some isomorphic simple groups, we prove that if $G$ has a non-trivial $A$-invariant normal subgroup $N$ such that $N\leq M$ and every non-nilpotent maximal $A$-invariant subgroup $K$ of $G$ not containing $N$ has index a prime-power and the projective special linear group $PSL_2(7)$ is not a composition factor of $G$, then $G$ is solvable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite groups in which some particular non-nilpotent maximal invariant subgroups have indices a prime-power Shi, Jiangtao Shan, Mengjiao Xu, Fanjie Group Theory 20D10 Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms, assume that $G$ has a maximal $A$-invariant subgroup $M$ that is a direct product of some isomorphic simple groups, we prove that if $G$ has a non-trivial $A$-invariant normal subgroup $N$ such that $N\leq M$ and every non-nilpotent maximal $A$-invariant subgroup $K$ of $G$ not containing $N$ has index a prime-power and the projective special linear group $PSL_2(7)$ is not a composition factor of $G$, then $G$ is solvable. |
| title | Finite groups in which some particular non-nilpotent maximal invariant subgroups have indices a prime-power |
| topic | Group Theory 20D10 |
| url | https://arxiv.org/abs/2502.03980 |