Plotkin’s Geometric Equivalence, Mal’cev’s Closure, and Incompressible Nilpotent Groups

Abstract

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