Geodesic
The finite groups with exactly four conjugate classes of maximal subgroups. II
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 86-91 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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, conjugate classes of maximal subgroups, $4M$-groups.
Mots-clés : nonsolvable group 
@article{SEMR_2018_15_a4,
     author = {V. A. Belonogov},
     title = {The finite groups with exactly four conjugate classes of maximal {subgroups.~II}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {86--91},
     year = {2018},
     volume = {15},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a4/}
}
TY  - JOUR
AU  - V. A. Belonogov
TI  - The finite groups with exactly four conjugate classes of maximal subgroups. II
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 86
EP  - 91
VL  - 15
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a4/
LA  - ru
ID  - SEMR_2018_15_a4
ER  - 
%0 Journal Article
%A V. A. Belonogov
%T The finite groups with exactly four conjugate classes of maximal subgroups. II
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 86-91
%V 15
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a4/
%G ru
%F SEMR_2018_15_a4
V. A. Belonogov. The finite groups with exactly four conjugate classes of maximal subgroups. II. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 86-91. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a4/

[1] G. Pazderski, “$\ddot{U}$ber maximal Untergruppen endlicher gruppen”, Math. Nachr., 26:6 (1964), 307–319 | MR | Zbl

[2] V. A. Belonogov, “Finite groups with three classes of maximal subgroups”, Math. USSR-Sb., 59:1 (1988), 223–236 | MR | Zbl

[3] V. A. Belonogov, “Finite groups with four classes of maximal subgroups. I”, Tr. Inst. mat. mech. UrO RAN, 23, no. 4, 2017, 52–62 | MR

[4] D. Gorenstein, R. Lyons, R. Solomon, The classification of the finite simple groups, Math. Surveys and Monographs, 40.1, AMS, 1994 | MR | Zbl

[5] M. Hall, Group theory, Izd. inostr. lit., M., 1962 | Zbl

[6] D. Gorenstein, Finite Groups, Harper Row, New York–London, 1968 | MR | Zbl

[7] B. Huppert, Endliche Gruppen, v. I, Springer, Berlin, 1967 | MR | Zbl

[8] J.H. Conway, R.T. Curtis, S.P. Norten, R.A. Parker, R.A. Wilson, Atlas of finite groups, Oxford University Press, Oxford, 1985 | MR | Zbl