Finite groups in which every maximal invariant subgroup of order divisible by $p$ is nilpotent

Jiangtao Shi; Mengjiao Shan; Fanjie Xu

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arXiv · 2502.06408

Finite groups in which every maximal invariant subgroup of order divisible by $p$ is nilpotent

Jiangtao Shi·Mengjiao Shan·Fanjie Xu

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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 provide a complete characterization of the structure of a group $G$ in which every maximal $A$-invariant subgroup of order divisible by $p$ is nilpotent.

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BibTeX RIS

Jiangtao Shi, Mengjiao Shan, Fanjie Xu. 2025-02-10. Finite groups in which every maximal invariant subgroup of order divisible by $p$ is nilpotent. https://arxiv.org/abs/2502.06408

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