J. Tang, B. Gao, J. Zhang, “On the structure of chief factors of finite groups with <nobr>${\cal m}_{p}$</nobr>-supplemented subgroups”, Sibirsk. Mat. Zh., 2020, Volume 61, Number 6,Pages <nobr>1411

On the structure of chief factors of finite groups with ${\cal m}_{p}$-supplemented subgroups

J. Tang^a, B. Gao^b, J. Zhang^c

^a Wuxi Institute of Technology Wuxi 214121, People's Republic of China
^b School of Mathematics and Statistics, Yili Normal University Yining 835000, People's Republic of China
^c School of Mathematics and Information, China West Normal University Nanchong 637009, People's Republic of China

Abstract: A subgroup $K$ of $G$ is ${\Cal M}_{p}$-supplemented in $G$ if there exists a subgroup $B$ of $G$ such that $G=KB$ and $TB<G$ for every maximal subgroup $T$ of $K$ with $|K:T|=p^{\alpha}$. We study the structure of the $G$-chief factors of finite groups below the normal subgroups of $G$ by using ${\Cal M}_{p}$-supplemented subgroups.

Keywords: ${\Cal M}_{p}$-supplemented subgroup, composition factor, chief factor, $p$-modular subgroup.

UDC: 512.542

MSC: 35R30

Received: 05.10.2019
Revised: 25.12.2019
Accepted: 19.02.2020

DOI: 10.33048/smzh.2020.61.613