Geometric equivalence of nilpotent groups

Nilpotent, torsion free groups are considered. Sufficient conditions are presented for a nilpotent, torsion free group to be geometrically equivalent to its Mal’tsev completion. Also some results are achieved in describing the classes of geometric equivalence of class 2 nilpotent, torsion free groups with center of small rank. Bibliography: 15 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 330, 2006, pp. 259–270.