  A group is CSA, if all of its maximal abelian subgroups are malnormal. It is
known that every non-abelian CSA group is an equational domain. We generalize
this result in two directions: we show that for a non-nilpotent group $G$ and a
fixed positive integer $k$, if all maximal elements in the set of class $k$
nilpotent subgroups of $G$ are malnormal, then $G$ is an equational domain.
Also, we prove that if a group $G$ is not locally nilpotent and if every
maximal locally nilpotent subgroup of $G$ is malnormal, then $G$ is an
equational domain.
