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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 5, Pages 1064–1073
DOI: https://doi.org/10.33048/smzh.2022.63.508 (Mi smj7713) 		 
On $\pi$-submaximal subgroups of minimal nonsolvable groups

A. V. Zavarnitsinea, D. O. Revinbca

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
c N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
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DOI: https://doi.org/10.33048/smzh.2022.63.508
Abstract: In 1979, Wielandt raised the problem of classifying the $\pi$-submaximal subgroups in minimal nonsolvable groups. Some solution to this problem is known for the minimal simple groups. We classify the $\pi$-submaximal subgroups of minimal nonsolvable groups whose Frattini subgroup is the minimal normal $2$-subgroup.
Keywords: minimal nonsolvable group, minimal simple group, $\pi$-maximal subgroup, $\pi$-submaximal subgroup.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0002
Russian Foundation for Basic Research 20-51-00007
The authors were supported by the RAS Program for Fundamental Research (Project FWNF–2022–0002) and the RFBR and BRFBR (Project 20–51–00007).
Received: 14.01.2022
Revised: 02.02.2022
Accepted: 15.04.2022
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 5, Pages 894–902
DOI: https://doi.org/10.1134/S0037446622050081
Document Type: Article
UDC: 512.542.6
MSC: 35R30
Language: Russian
Citation: A. V. Zavarnitsine, D. O. Revin, “On $\pi$-submaximal subgroups of minimal nonsolvable groups”, Sibirsk. Mat. Zh., 63:5 (2022), 1064–1073; Siberian Math. J., 63:5 (2022), 894–902
Citation in format AMSBIB
\Bibitem{ZavRev22}
\by A.~V.~Zavarnitsine, D.~O.~Revin
\paper On $\pi$-submaximal subgroups of minimal nonsolvable groups
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 5
\pages 1064--1073
\mathnet{http://mi.mathnet.ru/smj7713}
\crossref{https://doi.org/10.33048/smzh.2022.63.508}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 5
\pages 894--902
\crossref{https://doi.org/10.1134/S0037446622050081}
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