Geodesic
On $\frak F^{\omega}$-projectors and $\frak F^{\omega}$-covering subgroups of finite groups
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 24 (2024) no. 4, pp. 526-535 
M. M. Sorokina; D. G. Novikova. On $\frak F^{\omega}$-projectors and $\frak F^{\omega}$-covering subgroups of finite groups. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 24 (2024) no. 4, pp. 526-535. http://geodesic.mathdoc.fr/item/ISU_2024_24_4_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Only finite groups are considered. $\frak F$-projectors and $\frak F$-covering subgroups, where $\frak F$ is a certain class of groups, were introduced into consideration by W. Gaschutz as a natural generalization of Sylow and Hall subgroups in finite groups. Developing Gaschutz's idea, V. A. Vedernikov and M. M. Sorokina defined $\frak F^{\omega}$-projectors and $\frak F^{\omega}$-covering subgroups, where $\omega$ is a non-empty set of primes, and established their main characteristics. The purpose of this work is to study the properties of $\frak F^{\omega}$-projectors and $\frak F^{\omega}$-covering subgroups, establishing their relation with other subgroups in groups. The following tasks are solved: for a non-empty $\omega$-primitively closed homomorph $\frak F$ and a given set $\pi$ of primes, the conditions under which an $\frak F^{\omega}$-projector of a group coincides with its $\pi$-Hall subgroup are established; for a given formation $\frak F$, a relation between $\frak F^{\omega}$-covering subgroups of a group $G=A\rtimes B$ and $\frak F^{\omega}$-covering subgroups of the group $B$ is obtained. In the paper classical methods of the theory of finite groups, as well as methods of the theory of classes of groups are used.

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