On $p$-nilpotency of finite group with normally embedded maximal subgroups of some Sylow subgroups

Let $G$ be a finite group and $P$ be a $p$-subgroup of $G$. If $P$ is a Sylow subgroup of some normal subgroup of $G$, then we say that $P$ is normally embedded in $G$. Groups with normally embedded maximal subgroups of Sylow $p$-subgroup, where ${(|G|, p-1)=1}$, are studied. In particular, the $p$-nilpotency of such groups is proved.