Plotkin's geometric equivalence, Mal'cev's closure and incompressible nilpotent groups

In 1997 B. I. Plotkin introduced the notion of geometric equivalence of algebraic structures and posed the question: Is it true that every nilpotent torsion-free group is geometrically equivalent to its Mal'cev's closure? A negative answer was given by V. V. Bludov and B. V. Gusev in 2007 in the form of three counterexamples. In this paper we present an infinite series of counterexamples of unbounded Hirsch rank and nilpotency degree.