On S-quasinormally embedded subgroups of finite groups

Abstract

Let G be a finite group. A subgroup A is called:1) S-quasinormal in G if A is permutable with all Sylow subgroups in G 2) S-quasinormally embedded in G if every Sylow subgroup of A is a Sylow subgroup of some S-quasinormal subgroup of G. Let BseG be the subgroup generated by all the subgroups of B which are S-quasinormally embedded in G. A subgroup B is called SE-supplemented in G if there exists a subgroup T such that G = BT and B ∩ T ≤ BseG. The main result of the paper is the following.