Nilpotency of the derived subgroup of a finite group with semisubnormal Schmidt subgroups

A non-nilpotent finite group all of whose proper subgroups are nilpotent is called a Schmidt group. A subgroup $A$ is called seminormal in a group $G$ if there exists a subgroup $B$ such that $G=AB$ and $AB_1$ is a proper subgroup of $G$ for each proper subgroup $B_1$ of $B$. If $A$ is either subnormal in $G$ or seminormal in $G$, then the subgroup $A$ is called semisubnormal in $G$. We establish the nilpotency of the derived subgroup of a group all of whose Schmidt subgroups are semisubnormal.