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Matematicheskie Zametki, 2022, Volume 111, Issue 3, Pages 354–364
DOI: https://doi.org/10.4213/mzm13324
(Mi mzm13324)
 

This article is cited in 2 scientific papers (total in 2 papers)

Finite Groups with Three Nonconjugate Maximal Formational Subgroups

A. F. Vasil'ev, V. I. Murashka, A. K. Furs

Gomel State University named after Francisk Skorina
Full-text PDF (516 kB) Citations (2)
References:
Abstract: A constructive description is obtained for the hereditary $Z$-saturated formations $\mathfrak{F}$ of finite solvable groups containing every solvable group possessing three pairwise nonconjugate maximal subgroups belonging to $\mathfrak{F}$. It is proved that a finite group $G$ is supersolvable if it has three pairwise nonconjugate supersolvable maximal subgroups and its commutator subgroup $G'$ is nilpotent.
Keywords: finite group, maximal subgroup, $Z$-saturated formation, formation with the Belonogov property, formation with the Kegel property, supersolvable group.
Received: 18.10.2021
Revised: 30.11.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 3, Pages 356–363
DOI: https://doi.org/10.1134/S0001434622030038
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: A. F. Vasil'ev, V. I. Murashka, A. K. Furs, “Finite Groups with Three Nonconjugate Maximal Formational Subgroups”, Mat. Zametki, 111:3 (2022), 354–364; Math. Notes, 111:3 (2022), 356–363
Citation in format AMSBIB
\Bibitem{VasMurFur22}
\by A.~F.~Vasil'ev, V.~I.~Murashka, A.~K.~Furs
\paper Finite Groups with Three Nonconjugate Maximal Formational Subgroups
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 3
\pages 354--364
\mathnet{http://mi.mathnet.ru/mzm13324}
\crossref{https://doi.org/10.4213/mzm13324}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461266}
\transl
\jour Math. Notes
\yr 2022
\vol 111
\issue 3
\pages 356--363
\crossref{https://doi.org/10.1134/S0001434622030038}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129296968}
Linking options:
  • https://www.mathnet.ru/eng/mzm13324
  • https://doi.org/10.4213/mzm13324
  • https://www.mathnet.ru/eng/mzm/v111/i3/p354
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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