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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 1, Pages 116–122
DOI: https://doi.org/10.33048/smzh.2022.63.108 (Mi smj7645) 		 
On one criterion for the $\sigma$-nilpotency of a finite group

S. F. Kamornikova, V. N. Tyutyanovb

a Gomel State University named after Francisk Skorina
b Gomel Branch of International University "MITSO"
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DOI: https://doi.org/10.33048/smzh.2022.63.108
Abstract: Let $\mathfrak F$ be a class of groups and let $G$ be a finite group. We refer to a set $\Sigma$ of subgroups of $G$ as a $G$-covering subgroup system for a class $\mathfrak F$ if $G \in \mathfrak F$ whenever $\Sigma \subseteq \mathfrak F$. Also, we provide some nontrivial $G$-covering subgroup system for the class $\mathfrak F$ of all $\sigma$-nilpotent groups.
Keywords: finite group, Sylow subgroup, $G$-covering subgroup system, $\sigma$-nilpotent group.
Funding agency Grant number
Belarusian Republican Foundation for Fundamental Research Ф20Р–291
Ministry of Education of the Republic of Belarus 20211779
The first author was supported by the Ministry of Education of the Republic of Belarus (Grant no. 20211779). The second author was supported by the RFBR and BRFFR (Project F20R–291).
Received: 24.08.2021
Revised: 24.08.2021
Accepted: 11.10.2021
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 1, Pages 97–101
DOI: https://doi.org/10.1134/S0037446622010086
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: S. F. Kamornikov, V. N. Tyutyanov, “On one criterion for the $\sigma$-nilpotency of a finite group”, Sibirsk. Mat. Zh., 63:1 (2022), 116–122; Siberian Math. J., 63:1 (2022), 97–101
Citation in format AMSBIB
\Bibitem{KamTyu22}
\by S.~F.~Kamornikov, V.~N.~Tyutyanov
\paper On one criterion for the $\sigma$-nilpotency of a~finite group
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 1
\pages 116--122
\mathnet{http://mi.mathnet.ru/smj7645}
\crossref{https://doi.org/10.33048/smzh.2022.63.108}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4375017}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 1
\pages 97--101
\crossref{https://doi.org/10.1134/S0037446622010086}
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