Sylow numbers and the structure of finite groups

Huaquan Wei; Yi Chen; Hui Wu; Jiawen He

Sylow numbers and the structure of finite groups

Group Theory 2025-08-22 v1

Authors: Huaquan Wei , Yi Chen , Hui Wu , Jiawen He

Abstract

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 $dl(G/\Phi(G))$ of a solvable group $G$ . Some known results of Zhang in J. Algebra 1995, 176 are extended.

Keywords

Sylow numbers finite groups mutually permutable product p-length nilpotent length derived length

Cite

@article{arxiv.2508.15176,
  title  = {Sylow numbers and the structure of finite groups},
  author = {Huaquan Wei and Yi Chen and Hui Wu and Jiawen He},
  journal= {arXiv preprint arXiv:2508.15176},
  year   = {2025}
}

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Sylow numbers and the structure of finite groups

Abstract

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