Finite groups with restrictions on the Schmidt subgroups

Throughout the article, all groups are finite and $G$ always denotes a finite group. A subgroup $H$ of the group $G$ is called $\mathfrak{U}$-normal in $G$ if every chief factor of the group $G$ between $H^G$ and$H_G$ is cyclic. In this article, it is proved that if each Schmidt subgroup of the group $G$ is either subnormal or $\mathfrak{U}$-normal in $G$, then the derived subgroup $G'$ is nilpotent. Some well-known results are generalized.