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On the structure of chief factors of finite groups with ${\cal m}_{p}$-supplemented subgroups
J. Tanga, B. Gaob, J. Zhangc 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.
Received: 05.10.2019 Revised: 25.12.2019 Accepted: 19.02.2020
Citation:
J. Tang, B. Gao, J. Zhang, “On the structure of chief factors of finite groups with ${\cal m}_{p}$-supplemented subgroups”, Sibirsk. Mat. Zh., 61:6 (2020), 1411–1420; Siberian Math. J., 61:6 (2020), 1132–1139
Linking options:
https://www.mathnet.ru/eng/smj6059 https://www.mathnet.ru/eng/smj/v61/i6/p1411
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