# Rendiconti del Seminario Matematico della Università di Padova

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**Volume 124, 2010, pp. 231–246**

**DOI: 10.4171/RSMUP/124-16**

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

Vladimir O. Lukyanenko^{[1]}and Alexander N. Skiba

^{[2]}(1) Department of Mathematics, Gomel Francisk Skorina State University, 246019, Gomel, Belarus

(2) Department of Mathematics, Gomel Francisk Skorina State University, 246019, Gomel, Belarus

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.

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Lukyanenko Vladimir, Skiba Alexander: Finite Groups in which $\tau$-Quasinormality is a Transitive Relation. *Rend. Sem. Mat. Univ. Padova* 124 (2010), 231-246. doi: 10.4171/RSMUP/124-16