UNIVERSALLY EQUIVALENT SOLVABLE GROUPS

Every group that is finitely presented in the variety A^n of solvable groups, and is universally equivalent to a free group Fr(A^n) in this variety, is embedded in the Cartesian degree of F2(A^n). All subgroups on a set of two generators in that Cartesian degree which are universally equivalent to F2(A^n) are determined. Free solvable and nilpotent groups are proved universally equivalent.