A defining property of virtually nilpotent groups

We answer the question: which property distinguishes the virtually nil- potent groups among the locally graded groups? The common property of each finitely generated group to have a finitely generated commutator subgroup is not sufficient. However, the finitely generated commutator subgroup of F ₂(varG), a free group of rank 2 in the variety defined by G, is the necessary and sufficient condition.