On the equationally Artinian groups

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.