ON WEAKLY SS-QUASINORMAL SUBGROUPS OF FINITE GROUPS

Abstract

Let H be a subgroup of a finite group G, then we say that H is weakly SS-quasinormal in G, if there exists a normal subgroup T of G such that HT is s-permutable and H ∩ T is SS-quasinormal in G.  In this paper, we investigate the influence of some weakly SS-quasinormal subgroups on the structure of G.  Some new criterias about the p-nilpotency and supersolubility of a finite group were obtained.  We also generalized some known results about formations.