Geodesic
Finite groups with systems of $N$-quasinormal subgroups
Problemy fiziki, matematiki i tehniki, no. 2 (2024), pp. 79-83.

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

Throughout the article, all groups are finite and $G$ always denotes a finite group. A subgroup $A$ of a group $G$ is called quasinormal in $G$ if $AH = HA$ for all subgroups $H$ of $G$. If $A$ is a subgroup of $G$, then $A_{qG}$ is the subgroup of $A$ generated by all those subgroups of $A$ that are quasinormal in $G$. We say that the subgroup $A$ is $N$-quasinormal in $G$ ($N\geqslant G$), if for some quasinormal subgroup of $T$ of $G$, containing $A$, $N$ avoids the pair $(T, A_{qG})$, i. e. $N\cap T=N\cap A_{qG}$. Using these concepts, we give new characterizations of soluble and supersoluble finite groups.
Keywords: finite group, supersoluble group, subgroup lattice, quasinormal subgroup, modular lattice.
Mots-clés : soluble group 
@article{PFMT_2024_2_a13,
     author = {N. S. Kosenok and I. V. Bliznets and I. A. Sobol and Ya. A. Kuptsova},
     title = {Finite groups with systems of $N$-quasinormal subgroups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {79--83},
     publisher = {mathdoc},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2024_2_a13/}
}
TY  - JOUR
AU  - N. S. Kosenok
AU  - I. V. Bliznets
AU  - I. A. Sobol
AU  - Ya. A. Kuptsova
TI  - Finite groups with systems of $N$-quasinormal subgroups
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2024
SP  - 79
EP  - 83
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2024_2_a13/
LA  - ru
ID  - PFMT_2024_2_a13
ER  - 
%0 Journal Article
%A N. S. Kosenok
%A I. V. Bliznets
%A I. A. Sobol
%A Ya. A. Kuptsova
%T Finite groups with systems of $N$-quasinormal subgroups
%J Problemy fiziki, matematiki i tehniki
%D 2024
%P 79-83
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2024_2_a13/
%G ru
%F PFMT_2024_2_a13
N. S. Kosenok; I. V. Bliznets; I. A. Sobol; Ya. A. Kuptsova. Finite groups with systems of $N$-quasinormal subgroups. Problemy fiziki, matematiki i tehniki, no. 2 (2024), pp. 79-83. http://geodesic.mathdoc.fr/item/PFMT_2024_2_a13/

[1] R. Schmidt, Subgroup Lattices of Groups, Walter de Gruyter, Berlin, 1994 | MR | Zbl

[2] O. Ore, “Contributions in the theory of groups of finite order”, Duke Math J., 5 (1939), 431-460 | MR | Zbl

[3] Zh. Wang, A-Ming Liu, V.G. Safonov, A.N. Skiba, “A characterization of soluble PST-groups”, Bull. Austral. Math. Soc. (to appear)

[4] A-Ming Liu, Zh. Wang, V.G. Safonov, A.N. Skiba, “Characterization of $\sigma$-soluble P$\sigma$T-groups”, J. Group Theory (to appear)

[5] K. Doerk, T. Hawkes, Finite Soluble Groups, Walter de Gruyter, Berlin–New York, 1992 | MR

[6] A.N. Skiba, “On sublattices of the subgroup lattice defined by formation Fitting sets”, J. Algebra, 181 (2020), 69-85 | DOI | MR