Geodesic
Finite groups with $s$-normal maximal subgroups
Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 53-55.

Voir la notice de l'article provenant de la source Math-Net.Ru

Subgroup $H$ of $G$ is called $s$-normal in $G$, if $G$ has a subnormal subgroup $T$ such that $G=HT$ and $H\cap T\subseteq H_{\dots G}$. New criteria for the $p$-solvability and solvability of finite groups are obtained on the basis of this definition.
Keywords: finite group, maximal subgroup, subnormal subgroup.
Mots-clés : solvable group 
@article{PFMT_2015_2_a7,
     author = {N. S. Kosenok},
     title = {Finite groups with $s$-normal maximal subgroups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {53--55},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_2_a7/}
}
TY  - JOUR
AU  - N. S. Kosenok
TI  - Finite groups with $s$-normal maximal subgroups
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2015
SP  - 53
EP  - 55
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2015_2_a7/
LA  - ru
ID  - PFMT_2015_2_a7
ER  - 
%0 Journal Article
%A N. S. Kosenok
%T Finite groups with $s$-normal maximal subgroups
%J Problemy fiziki, matematiki i tehniki
%D 2015
%P 53-55
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2015_2_a7/
%G ru
%F PFMT_2015_2_a7
N. S. Kosenok. Finite groups with $s$-normal maximal subgroups. Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 53-55. http://geodesic.mathdoc.fr/item/PFMT_2015_2_a7/

[1] W. E. Deskins, “On maximal subgroups”, Proc. Symp. Pure Math., 1, 1959, 100–104 | MR | Zbl

[2] L. A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978, 272 pp. | MR

[3] K. Doerk, T. Hawkes, Finite soluble groups, Walter de Gruyter, Berlin–New York, 1992, 889 pp. | MR

[4] D. Robinson, A course in the theory of groups, Springer-Verlag, New York–Heidelberg–Berlin, 1982, 502 pp. | MR | Zbl

[5] M. V. Selkin, Maksimalnye podgruppy v teorii klassov konechnykh grupp, Belaruskaya navuka, Minsk, 1997, 144 pp. | MR

[6] S. F. Kamornikov, “K teoreme F. Kholla”, Voprosy algebry, 1990, no. 5, 45–52 | MR

[7] V. S. Monakhov, E. E. Gribovskaya, “O maksimalnykh i silovskikh podgruppakh konechnykh razreshimykh grupp”, Matematicheskie zametki, 70:4 (2001), 603–612 | MR | Zbl

[8] J. G. Thompson, “Finite groups with fixed-point-free automorphisms of prime order”, Proc Nat. Acad. Sci. USA, 45 (1959), 578–581 | MR | Zbl

[9] Z. Janko, “Finite groups with a nilpotent maximal subgroup”, J. Austral. Math. Soc., 4 (1964), 449–451 | MR | Zbl

[10] W. E. Deskins, “A condition for solvability of a finite group”, Illinois J. Math., 5 (1961), 306–313 | MR | Zbl

[11] Y. Wang, “$c$-Normality of groups and its properties”, J. Algebra, 180 (1996), 954–965 | MR | Zbl

[12] L. Zhu, W. Guo, K. P. Shum, “Weakly $c$-normal subgroups of finite groups and their properties”, Comm. Algebra, 30 (2002), 5505–5512 | MR | Zbl

[13] J. Lafuente, “Eine Note uber nichtabelsche Hauptfactoren und maximale Untergruppen einer endlichen Gruppe”, Comm. Algebra, 13:9 (1985), 2025–2036 | MR | Zbl