Topological Rank of (-1, 1) Metabelian Algebras

In 1981, Pchelintsev developed the idea for arranging non-nilpotent subvarieties in a given variety by using topological rank for spechtian varieties of algebra as a fixed tool. In this paper we show that for a given topological rank over a field of 2, 3 - torsion free of (-1, 1) metabelian algebra solvable of index 2 that are Lie-nilpotent of step not more than p is equal to P.