On F^ω-projectors and F^ω-covering subgroups of finite groups
Autor: | Sorokina, Marina M., Novikova, Diana G. |
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Jazyk: | English<br />Russian |
Rok vydání: | 2024 |
Předmět: | |
Zdroj: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, Vol 24, Iss 4, Pp 526-535 (2024) |
Druh dokumentu: | article |
ISSN: | 1816-9791 2541-9005 |
DOI: | 10.18500/1816-9791-2024-24-4-526-535 |
Popis: | 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. |
Databáze: | Directory of Open Access Journals |
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