  In this article, we study the property of being equationally Artinian in
groups. We prove that a finite extension of an equationally Artinian group is
again equationally Artinian. We also show that a quotient of an equationally
Artinian group of the form $G[t]$ by a normal subgroup which is a finite union
of radicals, is again equationally Artnian. This provides a large class of
examples of equationally Artinian groups.
