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

A subgroup Hof a finite group Gis said to be c-normal in Gif there exists a normal subgroup Nof Gsuch that HN=Gand H∩ N≤ H G =core G(H).In this paper we shall investigate the influence of c-normality of some subgroups on the strcture of finite groups further, and obtain some results on some kinds of weaker conditions.