Preview

Proceedings of the Institute of Mathematics of the NAS of Belarus

Advanced search

Finite partially soluble groups with transitive π-quasinormality relation for subgroups

Abstract

Throughout the article, all groups are finite. We say that a subgroup $A$ of $G$ is $\pi$-quasinormal in $G$, if $A$ is $1 \pi$-subnormal and modular in $G$. We prove that if the group $G$ is $\pi _{0}$-solvable, where $\pi _{0}=\pi (D) $ and $D$ is the $\pi $-special residual of $G$, and $\pi$-quasi-normality is a transitive relation in $G$, then $D$ is an abelian Hall subgroup of odd order in $G$.

For citations:


Dergacheva I.M., Zadorozhnyuk E.A., Shabalina I.P. Finite partially soluble groups with transitive π-quasinormality relation for subgroups. Trudy Instituta matematiki. 2023;31(2):28-33. (In Russ.)

Views: 61


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 1812-5093 (Print)