PreprintarXiv licencearXiv
On c-Normal Maximal Chains of Sylow Subgroups in Finite Groups
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∩ N≤ HG, where HG is the core of H in G. Let P be a nontrivial p-group. A chain of subgroups 1=P0 <P1<⋯ Pn−1<Pn=P is called a maximal chain of P provided that |Pi:Pi−1|=p for i=1,2,… 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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BibTeX
@misc{meng2026cnormal,
title = {{On $c$-Normal Maximal Chains of Sylow Subgroups in Finite Groups}},
author = {Wei Meng and Feiyu Geng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26968},
eprint = {2610.26968},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26968},
}
RIS
TY - UNPB
TI - On c-Normal Maximal Chains of Sylow Subgroups in Finite Groups
AU - Wei Meng
AU - Feiyu Geng
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.26968
UR - https://arxiv.org/abs/2610.26968
AB - 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∩ N≤ 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<⋯ 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,… 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.
ER -