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arXiv · 2610.26968

On $c$-Normal Maximal Chains of Sylow Subgroups in Finite Groups

Wei Meng·Feiyu Geng
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Abstract

Let $G$ be finite group. A subgroup $H$ of $G$ is said to be $c$-normal in $G$ if there exists a normal subgroup $N$ of $G$ such that $G = HN$ and $H\cap N\leq H_G$, where $H_G$ is the core of $H$ in $G$. Let $P$ be a nontrivial $p$-group. A chain of subgroups $1=P_0 <P_1<\cdots P_{n-1}<P_n=P$ is called a maximal chain of $P$ provided that $|P_i:P_{i-1}|=p$ for $i=1,2,\ldots n-1$. In this paper, we determine the structure of finite groups having $c$-normal subgroups of of a maximal chain of Sylow subgroups. We obtain new characterizations of finite $p$-nilpotent and supersolvable groups.

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Wei Meng, Feiyu Geng. 2026-10-18. On $c$-Normal Maximal Chains of Sylow Subgroups in Finite Groups. https://arxiv.org/abs/2610.26968

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