Geodesic
Finite groups with systems of $N$-quasinormal subgroups
Problemy fiziki, matematiki i tehniki, no. 2 (2024), pp. 79-83 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 
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     title = {Finite groups with systems of $N$-quasinormal subgroups},
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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/

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