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Matematicheskie Zametki, 2022, Volume 111, Issue 2, Pages 233–240
DOI: https://doi.org/10.4213/mzm13235 (Mi mzm13235) 		 
$G$-Covering Subgroup Systems for the Class of All $\sigma$-Nilpotent Finite Groups

X. Yia, S. F. Kamornikovb, V. N. Tyutyanovc

a Zhejiang University of Technology
b Gomel State University named after Francisk Skorina
c International University "MITSO"
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DOI: https://doi.org/10.4213/mzm13235
Abstract: Let $\mathfrak F$ be a nonempty class of groups and let $G$ be a finite group. A set $\Sigma$ of subgroups of the group $G$ is called a $G$-covering subgroup system for the class $\mathfrak F$ (or an $\mathfrak F$-covering subgroup system of $G$) if $\Sigma \subseteq \mathfrak F$ always implies that $G \in \mathfrak F$. In this paper, a nontrivial set of subgroups of $G$ is constructed which is a $G$-covering subgroup system for the class $\mathfrak F$ of all $\sigma$-nilpotent groups.
Keywords: finite group, Sylow subgroup, supplement to a subgroup, $G$-covering subgroup system, $\sigma$-nilpotent group.
Funding agency Grant number
Zhejiang Provincial Natural Science Foundation of China LY18A010028
Ministry of Education of the Republic of Belarus 20211779
Belarusian Republican Foundation for Fundamental Research Ф20Р-291
The research of the first author was supported by Zhejiang Provincial Natural Science Foundation of China (grant no. LY18A010028). The research of the second author was financially supported by the Ministry of Education of the Republic of Belarus (grant no. 20211779). The research of the third author was supported by the Russian Foundation for Basic Research and by the Belarusian Republican Foundation for Fundamental Research within the framework of the scientific grant no. F20R-291.
Received: 25.07.2021
Revised: 04.09.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 2, Pages 230–235
DOI: https://doi.org/10.1134/S0001434622010266
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: X. Yi, S. F. Kamornikov, V. N. Tyutyanov, “$G$-Covering Subgroup Systems for the Class of All $\sigma$-Nilpotent Finite Groups”, Mat. Zametki, 111:2 (2022), 233–240; Math. Notes, 111:2 (2022), 230–235
Citation in format AMSBIB
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\pages 233--240
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