The influence of c-normality of subgroups on the structure of finite groups

A subgroup H of a finite group G is said to be c-normal in G if there is a normal subgroup N of G such that HN=G and H∩N≤HG=coreG(H). In this paper we investigate further the influence of c-normality of some subgroups on the structure of finite groups and generalize some known results.