On a finite group in which every non-nilpotent maximal invariant subgroup of order divisible by $p$ is normal
Year: 2026
Type: preprint
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 $|G|$.
Source: arXiv (Cornell University)
Authors: Shi, Jiangtao, Li, Fanghua, Li, Na
Institutions: Yantai University, Zaozhuang University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G3449648125, G4610495414
OpenAlex ID: W7223271438