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arXiv · 2610.30653

On a finite group in which every non-nilpotent maximal invariant subgroup of order divisible by $p$ is normal

Jiangtao Shi·Fanghua Li·Na Li
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Abstract

Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms. For any fixed prime divisor $p$ of $|G|$, we prove that if every non-nilpotent maximal $A$-invariant subgroup of $G$ of order divisible by $p$ is normal then $G$ has 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, Na Li. 2026-10-22. On a finite group in which every non-nilpotent maximal invariant subgroup of order divisible by $p$ is normal. https://arxiv.org/abs/2610.30653

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