# Finite Groups in which $\tau$-Quasinormality is a Transitive Relation

### Vladimir O. Lukyanenko

Gomel Francisk Skorina State University, Belarus### Alexander N. Skiba

Gomel Francisk Skorina State University, Belarus

## Abstract

Let *H* be a subgroup of a finite group *G*. We say that *H*is $\tau$-*quasinormal* *in* *G* if *HP* = *PH* for all Sylow*p*-subgroups *P* of *G* such that (|*H*|,*p*) = 1 and (|*H*|, |*P__G*|) ≠ 1.In this article, finite groups in which $\tau$-quasinormality is a transitive relation are described.

## Cite this article

Vladimir O. Lukyanenko, Alexander N. Skiba, Finite Groups in which $\tau$-Quasinormality is a Transitive Relation. Rend. Sem. Mat. Univ. Padova 124 (2010), pp. 231–246

DOI 10.4171/RSMUP/124-16