The in uence of partially τ -quasinormal subgroups on the structure of finite groups

Abstract

A subgroup H of a group G is said to be τ -quasinormal in G if Hpermutes with every Sylow subgroup Q of G such that (|H|, |Q|) = 1and (|H|, |QG|) 6= 1; H is called partially τ -quasinormal in G if G has anormal subgroup T such that HT is S-quasinormal in G and H ∩ T ≤HτG, where HτG is the subgroup generated by all those subgroups ofH which are τ -quasinormal in G. In this paper, we investigate theinuence of some partially τ -quasinormal subgroups on the structureof nite group. Some new characterizations of p-supersoluble and pnilpotentgroups are obtained.