FINITE GROUPS WITH WEAKLY S-QUASINORMALLY EMBEDDED SUBGROUPS

Let H be a subgroup of a group G. A subgroup H of G is said to be S-quasinormally embedded in G if for each prime p dividing |H|, a Sylow p-subgroup of H is also a Sylow p-subgroup of some S-quasinormal subgroup of G. We say that H is weakly S-quasinormally embedded in G if there exists a normal subgroup T of G such that HT ⊴ G and H ∩ T is S-quasinormally embedded in G. In this paper, we investigate further the influence of weakly S-quasinormally embedded subgroups on the structure of finite groups. A series of known results are generalized.