Decidability boundaries for some classes of nilpotent and solvable groups

For any natural k ≥ 3 and l ≥ 2, we describe decidability boundaries for two varieties: the variety of all k-nilpotent groups and the variety of all l-solvable groups. Translated fromAlgebra i Logika, Vol. 39, No. 2, pp. 127–133, March–April, 2000.