MATHEMATICS

On Hall subgroups of finite groups

V. O. Lukyanenko

P.O. Sukhoi Gomel State Technical University

Abstract: Let $G$ be a finite group and $H$ a subgroup of $G$. Then $H$ is said to be $\tau$-quasinormal in $G$ if $H$ permutes with all Sylow subgroups $\mathcal{Q}$ of $G$ such that $(|H|, |\mathcal{Q}|)=1$ and $(|H|, |\mathcal{Q}^G|)\ne1$. A generalization of Schur–Zassenhaus Theorem in terms of $\tau$-quasinormal subgroups is obtained.

Keywords: $\tau$-quasinormal subgroup, Sylow subgroup, Hall subgroup, soluble group.

UDC: 512.542

Received: 19.05.2016

Language: English