Sylow numbers and the structure of finite groups
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918128270704640 |
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| author | Wei, Huaquan Chen, Yi Wu, Hui He, Jiawen |
| author_facet | Wei, Huaquan Chen, Yi Wu, Hui He, Jiawen |
| contents | Suppose that the finite group $G=AB$ is a mutually permutable product of two subgroups $A$ and $B$. By using Sylow numbers of $A$ and $B$, we present some new bounds of the $p$-length $l_p(G)$ of a $p$-solvable group $G$ and the nilpotent length $F_l(G)$ and the derived length $dl(G/Φ(G))$ of a solvable group $G$. Some known results of Zhang in J. Algebra 1995, 176 are extended. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sylow numbers and the structure of finite groups Wei, Huaquan Chen, Yi Wu, Hui He, Jiawen Group Theory 20D10, 20D20 Suppose that the finite group $G=AB$ is a mutually permutable product of two subgroups $A$ and $B$. By using Sylow numbers of $A$ and $B$, we present some new bounds of the $p$-length $l_p(G)$ of a $p$-solvable group $G$ and the nilpotent length $F_l(G)$ and the derived length $dl(G/Φ(G))$ of a solvable group $G$. Some known results of Zhang in J. Algebra 1995, 176 are extended. |
| title | Sylow numbers and the structure of finite groups |
| topic | Group Theory 20D10, 20D20 |
| url | https://arxiv.org/abs/2508.15176 |