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 $G$.
About the Authors
I. M. Dergacheva
Белорусский государственный университет транспорта
Belarus
Belarus
E. A. Zadorozhnyuk
Белорусский государственный университет транспорта
Belarus
Belarus
I. P. Shabalina
Белорусский государственный университет транспорта
Belarus
Belarus
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Review
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.)
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