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A group is CSA, if all of its maximal abelian subgroups are malnormal. It isknown that every non-abelian CSA group is an equational domain. We generalizethis result in two directions: we show that for a non-nilpotent group $G$ and afixed 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 everymaximal locally nilpotent subgroup of $G$ is malnormal, then $G$ is anequational domain.

New classes groups which are equational domains