  It is an open question in the study of Chermak-Delgado lattices precisely
which finite groups $G$ have the property that $CD(G)$ is a chain of length
$0$. In this note, we determine two classes of groups with this property. We
prove that if $G=AB$ is a finite group, where $A$ and $B$ are abelian subgroups
of relatively prime orders with $A$ normal in $G$, then the Chermak-Delgado
lattice of $G$ equals $\{AC_B(A)\}$, a strengthening of earlier known results.
