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

Vladimir O. Lukyanenko; Alexander N. Skiba

doi:10.4171/rsmup/124-16

JournalsrsmupVol. 124pp. 231–246

Finite Groups in which $τ$ -Quasinormality is a Transitive Relation

Vladimir O. Lukyanenko
Gomel Francisk Skorina State University, Belarus
Alexander N. Skiba
Gomel Francisk Skorina State University, Belarus

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

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Abstract

Let $H$ be a subgroup of a finite group $G$ . We say that $H$ is $τ$ -quasinormal in $G$ if $H P = P H$ for all Sylow $p$ -subgroups $P$ of $G$ such that $(∣ H ∣, p) = 1$ and $(∣ H ∣, ∣ P_{G} ∣) \neq = 1$ . In this article, finite groups in which $τ$ -quasinormality is a transitive relation are described.

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

DOI 10.4171/RSMUP/124-16