A note on the Π-property of some subgroups of finite groups

Let H be a subgroup of a finite group G. We say that H satisfies the Π-property in G if for any chief factor $ L / K $ of G, |G/K : NG/K(HK/K∩ L/K )| is a π (HK/K∩ L/K)-number. In this paper, we obtain some criteria for the p-supersolubility or p-nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the Π-property.