Finitely presented solvable groups and Lie algebras with unsolvable equality problem

Abstract

We will use the following standard notation: 91 is the variety of Abelian groups, ~c the variety of nilpotent groups of nilpotency degree ~c, 9~ n the variety of solvable groups of derived length ~n. If ~ is some variety of groups, then Z'~ will denote the variety of groups whose quotient by the center belong to ~. We let-~i~2 denote the product of the varieties ~i and ~2. The same notation will be used for the corresponding varieties of Lie algebras. In addition, we will denote by 9~m the variety of all Abelian groups of exponent m.