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arXiv · 2611.02596

On a finite group in which every maximal subgroup of order divisible by $p$ containing the normalizer of some Sylow subgroup is nilpotent

Jiangtao Shi·Fanghua Li
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Abstract

Let $G$ be a finite group and $p$ any fixed prime divisor of $|G|$. We prove that if every maximal subgroup of $G$ of order divisible by $p$ containing the normalizer of some Sylow subgroup is nilpotent then $G$ is a solvable group having a Sylow tower and $G$ is $q$-nilpotent or $q$-closed for each prime divisor $q$ of $|G|$.

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Jiangtao Shi, Fanghua Li. 2026-11-02. On a finite group in which every maximal subgroup of order divisible by $p$ containing the normalizer of some Sylow subgroup is nilpotent. https://arxiv.org/abs/2611.02596

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