Geodesic
On $p$-nilpotency of one class of finite groups
Problemy fiziki, matematiki i tehniki, no. 3 (2013), pp. 61-65

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A subgroup $H$ of a group $G$ is called modular in $G$ if $H$ is a modular element (in sense of Kurosh) of the lattice $L(G)$ of all subgroups of $G$. The subgroup of $H$ generated by all modular subgroups of $G$ contained in $H$ is called the modular core of $H$ and denoted by $H_{mG}$. In the paper a new criterion of the $p$-nilpotency of a group was obtained on the basis of the concept of the $m$-supplemented subgroup which is the extension of concepts of modular and supplemented subgroups respectively.
Keywords: finite group, $p$-nilpotent group, modular subgroup, modular core, $m$-supplemented subgroup, maximal subgroup, cyclic subgroup, Sylow $p$-subgroup. 
@article{PFMT_2013_3_a9,
     author = {V. A. Vasil'ev},
     title = {On $p$-nilpotency of one class of finite groups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {61--65},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2013_3_a9/}
}
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V. A. Vasil'ev. On $p$-nilpotency of one class of finite groups. Problemy fiziki, matematiki i tehniki, no. 3 (2013), pp. 61-65. http://geodesic.mathdoc.fr/item/PFMT_2013_3_a9/