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

Jiangtao Shi; Mengjiao Shan; Fanjie Xu

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

Group Theory 2025-02-11 v1

Authors: Jiangtao Shi , Mengjiao Shan , Fanjie Xu

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.

Keywords

finite groups maximal invariant subgroup nilpotent coprime action prime divisor

Cite

@article{arxiv.2502.06408,
  title  = {Finite groups in which every maximal invariant subgroup of order divisible by $p$ is nilpotent},
  author = {Jiangtao Shi and Mengjiao Shan and Fanjie Xu},
  journal= {arXiv preprint arXiv:2502.06408},
  year   = {2025}
}

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