Equationally Noetherian group

Definition
A group is said to be equationally Noetherian if every system of equations over the group involving finitely many variables is equivalent to a finite subsystem.

Facts

 * Inner automorphism group of equationally Noetherian group is equationally Noetherian
 * Equationally Noetherian subgroup of finite index implies equationally Noetherian

Other uses

 * Two theorems about equationally Noetherian groups