MATHEMATICS

Finite groups with given systems of quasipermutable subgroups

V. A. Kovaleva, Zh. Xiaoyu

F. Scorina Gomel State University, Gomel

Abstract: Let $G$ be a finite group. A subgroup $A$ of $G$ is said to be quasipermutable in $G$ if A either covers or avoids every maximal pair $(K,H)$ of $G$. We study the finite groups with given systems of quasipermutable subgroups.

Keywords: finite group, maximal pair, (weakly) quasipermutable subgroup, generalized Fitting subgroup, $p$-nilpotent group, $\mathcal{U}$-hypercentre.

UDC: 512.542

Received: 17.05.2012

Language: English