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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, Volume 27, Number 1, Pages 98–102
DOI: https://doi.org/10.21538/0134-4889-2021-27-1-98-102 (Mi timm1794) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On two problems from “The Kourovka Notebook”

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/10.21538/0134-4889-2021-27-1-98-102
Abstract: We solve Problems 19.87 and 19.88 formulated by A.N. Skiba in “The Kourovka Notebook.” It is proved that if, for every Sylow subgroup $P$ of a finite group $G$ and every maximal subgroup $V$ of $P$, there is a $\sigma$-soluble ($\sigma$-nilpotent) subgroup $T$ such that $VT=G$, then $G$ is $\sigma$-soluble ($\sigma$-nilpotent, respectively).
Keywords: finite group, $\sigma$-soluble group, $\sigma$-nilpotent group, partition of the set of all prime numbers, Sylow subgroup, maximal subgroup.
Funding agency Grant number
Belarusian Republican Foundation for Fundamental Research Ф20Р-291
This work was supported by the Russian Foundation for Basic Research and the Belarusian Republican Foundation for Fundamental Research (project no. F20R-291).
Received: 17.01.2021
Revised: 10.02.2021
Accepted: 18.02.2021
Bibliographic databases:
Document Type: Article
UDC: 512.542
MSC: 20D10, 0D15, 20D30
Language: Russian
Citation: S. F. Kamornikov, V. N. Tyutyanov, “On two problems from “The Kourovka Notebook””, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 1, 2021, 98–102
Citation in format AMSBIB
\Bibitem{KamTyu21}
\by S.~F.~Kamornikov, V.~N.~Tyutyanov
\paper On two problems from ``The Kourovka Notebook''
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2021
\vol 27
\issue 1
\pages 98--102
\mathnet{http://mi.mathnet.ru/timm1794}
\crossref{https://doi.org/10.21538/0134-4889-2021-27-1-98-102}
\elib{https://elibrary.ru/item.asp?id=44827397}
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