Some Equivalent Conditions for c-normal Subgroups

c-normal subgroups and weakly c-normal subgroups play an important role in finite groups.A c-normal subgroup of G must be a weakly c-normal subgroup,but the converse is not ture in general.Many important results about finite group have been abtained by use the c-normality of subgroups.But the weakly c-normal subgroups are not the case,through the impact of c-normal subgroups and weakly c-normal subgroups on the structure of finite groups ,some sufficient conditions for a weakly c-normal subgroup to be c-normal were given.