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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 6, Pages 1411–1420
DOI: https://doi.org/10.33048/smzh.2020.61.613 (Mi smj6059) 		 
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
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DOI: https://doi.org/10.33048/smzh.2020.61.613
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.
Funding agency Grant number
National Natural Science Foundation of China 11701223
Natural Science Foundation of Jiangsu Province BK20181451
Фондами фундаментальных исследований Китайского западного нормального университета 17E091
Фондами фундаментальных исследований Китайского западного нормального университета 18B032
Фонд университетских исследовательских проектов Синцзян-Уйгурского автономного района XJEDU2017M034
This research is supported by the grant of NSFC (Grant #11701223), University Research Projects Funds of the Xinjiang Uygur Autonomous Region (Grant #XJEDU2017M034), and the Fundamental Research Funds of China West Normal University (17E091 and 18B032).
Received: 05.10.2019
Revised: 25.12.2019
Accepted: 19.02.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 6, Pages 1132–1139
DOI: https://doi.org/10.1134/S0037446620060130
Bibliographic databases:
Document Type: Article
UDC: 512.542
MSC: 35R30
Language: Russian
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
Citation in format AMSBIB
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