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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 86–91 (Mi semr901)  

Mathematical logic, algebra and number theory

The finite groups with exactly four conjugate classes of maximal subgroups. II

V. A. Belonogov

Krasovskii Institute of Mathematics and Mechanics, S.Kovalevskaya str., 16, 620990, Yekaterinburg, Russia

Abstract: In this work we continue investigate the finite groups, having exactly four conjugate classes of maximal subgroups. The groups with this property we call $4M$-groups. The investigation of such groups was started in the part I where the simple $4M$-groups and as well nonsimple nonsolvable $4M$-groups without normal maximal subgroups were completely described. In the present part II we begin study the remaining case, in which a nonsolvable $4M$-group has a normal maximal subgroup. Here the early results of the author on the structure of the finite groups with exactly three conjugate classes of maximal subgroups and the results of G. Pazderski on the structure of the finite groups with exactly two conjugate classes of maximal subgroups are used.

Keywords: finite group, nonsolvable group, conjugate classes of maximal subgroups, $4M$-groups.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0387-2015-0060


DOI: https://doi.org/10.17377/semi.2018.15.010

Full text: PDF file (139 kB)
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Document Type: Article
UDC: 512.54
MSC: 20D05, 20E28
Received December 10, 2017, published February 7, 2018

Citation: V. A. Belonogov, “The finite groups with exactly four conjugate classes of maximal subgroups. II”, Sib. Èlektron. Mat. Izv., 15 (2018), 86–91

Citation in format AMSBIB
\Bibitem{Bel18}
\by V.~A.~Belonogov
\paper The finite groups with exactly four conjugate classes of maximal subgroups.~II
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 86--91
\mathnet{http://mi.mathnet.ru/semr901}
\crossref{https://doi.org/10.17377/semi.2018.15.010}


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