On weakly s-quasinormally embedded and ss-quasinormal subgroups of finite groups

Abstract

Suppose G is a finite group and H is a subgroup of G. H is called weakly s-quasinormally embedded in G if there are a subnormal subgroup T of G and an s-quasinormally embedded subgroup H se of G contained in H such that G = HT and H ∩ T ≤ H se ; H is called ss-quasinormal in G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. We investigate the influence of weakly s-quasinormally embedded and ss-quasinormal subgroups on the structure of finite groups. Some recent results are generalized.