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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.

UDC: 512.54

MSC: 20D05, 20E28

Received December 10, 2017, published February 7, 2018

DOI: 10.17377/semi.2018.15.010

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