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Sibirsk. Mat. Zh., 2018, Volume 59, Number 1, Pages 65–77 (Mi smj2954)  

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

Finite groups with three given subgroups

A. F. Vasil'eva, T. I. Vasil'evaab, K. L. Parfenkova

a Francisk Skorina Gomel State University, Gomel, Belarus
b Belarusian State University of Transport, Gomel, Belarus

Abstract: Given a hereditary saturated formation $\mathfrak F$ of soluble groups, we study finite groups with three $\mathfrak F$-subgroups of coprime indices. We obtain the new criteria for these groups to lie in the Shemetkov formations, the formations of all supersoluble groups, the formations of all groups with nilpotent commutator subgroup, and other formations.

Keywords: finite group, supersoluble group, $\mathrm w$-supersoluble group, formation, hereditary saturated formation, $\mathfrak F$-subnormal subgroup.

DOI: https://doi.org/10.17377/smzh.2018.59.106

Full text: PDF file (319 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2018, 59:1, 50–58

Bibliographic databases:

UDC: 512.542
MSC: 35R30
Received: 25.04.2017

Citation: A. F. Vasil'ev, T. I. Vasil'eva, K. L. Parfenkov, “Finite groups with three given subgroups”, Sibirsk. Mat. Zh., 59:1 (2018), 65–77; Siberian Math. J., 59:1 (2018), 50–58

Citation in format AMSBIB
\Bibitem{VasVasPar18}
\by A.~F.~Vasil'ev, T.~I.~Vasil'eva, K.~L.~Parfenkov
\paper Finite groups with three given subgroups
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 1
\pages 65--77
\mathnet{http://mi.mathnet.ru/smj2954}
\crossref{https://doi.org/10.17377/smzh.2018.59.106}
\elib{https://elibrary.ru/item.asp?id=32824587}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 1
\pages 50--58
\crossref{https://doi.org/10.1134/S0037446618010068}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043523172}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. S. Monakhov, A. A. Trofimuk, “Finite groups with two supersoluble subgroups”, J. Group Theory, 22:2 (2019), 297–312  crossref  mathscinet  zmath  isi  scopus
    2. A. F. Vasil'ev, V. I. Murashka, “Formations and Products of $\mathrm F(G)$-Subnormal Subgroups of Finite Solvable Groups”, Math. Notes, 107:3 (2020), 413–424  mathnet  crossref  crossref  mathscinet  isi  elib
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