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

Abstract

In this paper, we introduced a new concept of $p\tau $ 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 \cap K \leq H_{p\tau G} $ where $H_{p\tau G} $ generated by all those subgroups of H which are partially τ-quasinormal in G. We investigate the influence of some $p\tau $-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.

Keywords

• partially τ-quasinormal subgroup
• τ-quasinormal subgroup
• supersolvable group