Journal of Mathematical Sciences

, Volume 243, Issue 4, pp 601–611 | Cite as

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

  • G. A. NoskovEmail author

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.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsOmskRussia

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