A note on an extension of Shidov's theorem and Shlyk's theorem

Jiangtao Shi; Fanghua Li

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arXiv · 2611.02608

A note on an extension of Shidov's theorem and Shlyk's theorem

Jiangtao Shi·Fanghua Li

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Abstract

Let $G$ be a non-solvable group and $p$ any fixed prime divisor of $|G|$. We prove that the intersection of all non-nilpotent maximal subgroups of $G$ of order divisible by $p$ containing the normalizer of some Sylow subgroup is $p$-closed, which provides a further generalization of Shidov's theorem and Shlyk's theorem.

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Jiangtao Shi, Fanghua Li. 2026-11-02. A note on an extension of Shidov's theorem and Shlyk's theorem. https://arxiv.org/abs/2611.02608

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