On finite groups with Hall normally embedded Schmidt subgroups

A subgroup $H$ of a finite group $G$ is said to be Hall normally embedded in $G$ if there is a normal subgroup $N$ of $G$ such that $H$ is a Hall subgroup of $N$. A Schmidt group is a non-nilpotent finite group whose all proper subgroups are nilpotent. In this paper, we prove that if each Schmidt subgroup of a finite group $G$ is Hall normally embedded in $G$, then the derived subgroup of $G$ is nilpotent.