Geodesic
$G$-Covering Subgroup Systems for the Class of All $\sigma$-Nilpotent Finite Groups
Matematičeskie zametki, Tome 111 (2022) no. 2, pp. 233-240

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Let $\mathfrak F$ be a nonempty class of groups and let $G$ be a finite group. A set $\Sigma$ of subgroups of the group $G$ is called a $G$-covering subgroup system for the class $\mathfrak F$ (or an $\mathfrak F$-covering subgroup system of $G$) if $\Sigma \subseteq \mathfrak F$ always implies that $G \in \mathfrak F$. In this paper, a nontrivial set of subgroups of $G$ is constructed which is a $G$-covering subgroup system for the class $\mathfrak F$ of all $\sigma$-nilpotent groups.
Keywords: finite group, Sylow subgroup, supplement to a subgroup, $G$-covering subgroup system, $\sigma$-nilpotent group. 
@article{MZM_2022_111_2_a5,
     author = {X. Yi and S. F. Kamornikov and V. N. Tyutyanov},
     title = {$G${-Covering} {Subgroup} {Systems} for the {Class} of {All} $\sigma${-Nilpotent} {Finite} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {233--240},
     publisher = {mathdoc},
     volume = {111},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_2_a5/}
}
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X. Yi; S. F. Kamornikov; V. N. Tyutyanov. $G$-Covering Subgroup Systems for the Class of All $\sigma$-Nilpotent Finite Groups. Matematičeskie zametki, Tome 111 (2022) no. 2, pp. 233-240. http://geodesic.mathdoc.fr/item/MZM_2022_111_2_a5/