Finite groups in which strong 4-quasinormality is transitive relation

Abstract

Two subgroups H and K are 4-permutable in G if <H,K> = HKHK, and H is strong 4-quasinormal in G if H is 4-permutable with every subgroups K of G. A finite group G is called Sq4T-group if strong 4-quasinormality is transitive relation among the subgroup of G. In this paper we study finite Sq4T-groups. In particular, we prove that every Sq4T-group is solvable. Some facts related to 4-permutability and illustrating examples are also presented in this paper.