Geometrical equivalence of groups

The notion of geometrical equivalence of two algebras, which is basic for t his paper, is introduced in [5], [6]. It is motivated in the framework of u niversal algebraic geometry, in which algebraic varieties are considered in arbitrary varieties of algebras. Universal algebraic geometry (as well as classic algebraic geometry) studies systems of equations and its geometric images, i.e., algebraic varieties, consisting of solutions of equations. Ge ometrical equivalence of algebras means, in some sense, equal possibilities for solving systems of equations. In this paper we consider results about geometrical equivalence of algebras , and special attention is paled oil groups (abelian and nilpotent).