Influence of partially τ-embedded subgroups of prime power order in supersolubility and p-nilpotency of finite groups.

In this paper, we introduced a new concept of p τ embedded subgroups which belongs to an embedded class of subgroups of finite groups. A subgroup H of a group G is said to be a partially τ-embedded subgroup in G if there exists a normal subgroup K of G such that HK is normal in G and H ∩ K ≤ H p τ G where H p τ G generated by all those subgroups of H which are partially τ-quasinormal in G. We investigate the influence of some p τ -embedded subgroups with prime power order on the structure of a finite group G. Some new criteria about the p-nilpotency and supersolubility of a finite group were obtained. Our results also generalized some earlier ones about formations. [ABSTRACT FROM AUTHOR]