Ts-permutable Of The Subgroup

Through the study of the theory of finite groups, we know the structure of finite groups and their subgroups are closely related to the nature. On the properties of different subgroups of different structures can be a finite group.This article presented ts-permutable subgroups defined, and localized ts-permutable of subgroup.Let H be subnormal subgroup of a finite group G such that G/H is p-nilpotent, where p is a prime divisor of|G|with (|G|,p-1)= 1. If there exists a Sylow p-subgroup P of H such that every maximal subgroup of P is ts-permutable in N and either N'or P' is ts-permutable in G, then, G is p-nilpotent, where N=NG(H).