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Algebra Logika, 2004, Volume 43, Number 2, Pages 184–196 (Mi al63)  

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

An Analog for the Frattini Factorization of Finite Groups

V. I. Zenkova, V. S. Monakhovb, D. O. Revinc

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Francisk Skorina Gomel State University
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Using the classification of finite simple groups, we prove that if $H$ is an insoluble normal subgroup of a finite group $G$, then $H$ contains a maximal soluble subgroup $G$ such that $G=HN_G(S)$. Thereby Problem 14.62 in the “Kourovka Notebook” is given a positive solution. As a consequence, it is proved that in every finite group, there exists a subgroup that is simultaneously a ${\mathfrak S}$-projector and a ${\mathfrak S}$-injector in the class, ${\mathfrak S}$ , of all soluble groups.

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English version:
Algebra and Logic, 2004, 43:2, 102–108

Bibliographic databases:

UDC: 512.542
Received: 22.04.2002

Citation: V. I. Zenkov, V. S. Monakhov, D. O. Revin, “An Analog for the Frattini Factorization of Finite Groups”, Algebra Logika, 43:2 (2004), 184–196; Algebra and Logic, 43:2 (2004), 102–108

Citation in format AMSBIB
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\by V.~I.~Zenkov, V.~S.~Monakhov, D.~O.~Revin
\paper An Analog for the Frattini Factorization of Finite Groups
\jour Algebra Logika
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\issue 2
\pages 184--196
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\transl
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 2
\pages 102--108
\crossref{https://doi.org/10.1023/B:ALLO.0000020847.92969.e4}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42349098388}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Revin D.O. Vdovin E.P., “Frattini Argument For Hall Subgroups”, J. Algebra, 414 (2014), 95–104  crossref  mathscinet  zmath  isi  elib  scopus
    2. Guo W., Revin D.O., “Pronormality and Submaximal (Sic)-Subgroups on Finite Groups”, Commun. Math. Stat., 6:3, SI (2018), 289–317  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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