On $P$-property of subgroups of finite groups

Let $H$ be a subgroup of a group $G$. We say that $H$ has $P$-property in $G$ if $|G/K:N_{G/K}(HK/K\cap L/K)|$ is a $p$-number for any $pd$-chief factor $L/K$ of $G$. Using this property of subgroups, some new criterions of $p$-nilpotency of groups are obtained.