Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 86–91
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
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.
finite group, nonsolvable group, conjugate classes of maximal subgroups, $4M$-groups.
PDF file (139 kB)
MSC: 20D05, 20E28
Received December 10, 2017, published February 7, 2018
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
\paper The finite groups with exactly four conjugate classes of maximal subgroups.~II
\jour Sib. \`Elektron. Mat. Izv.
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