Finite groups with some σ-primary subgroups sσ-quasinormal

Abstract

Let G be a finite group, a partition of the set of all primes and A set of subgroups of G is said to be a complete Hall σ-set of G if every nonidentity member of is a Hall σi-subgroup of G for some and contains exactly one Hall σi-subgroup of G for every G is said to be σ-full if G possesses a complete Hall σ-set. We say a subgroup H of G is sσ-quasinormal (supplement-σ-quasinormal) in G if there exists a σ-full subgroup T of G such that G = HT and H permutes with every Hall σi-subgroup of T for all In this article, we obtain some results about the sσ-quasinormal subgroups and use them to determine the structure of finite groups. In particular, some new criteria of p-nilpotency, solubility, supersolubility of a group are obtained.