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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 470, Pages 147–161 (Mi znsl6617)  
Plotkin's geometric equivalence, Mal'cev's closure and incompressible nilpotent groups

G. A. Noskov

Sobolev Institute of Mathematics, 644043 Omsk, Russia
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Abstract: 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.
Key words and phrases: geometric equivalence, Mal’cev’s closure, incompressible nilpotent groups.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.1.1., 0314-2016-0004
The work was supported by the program of fundamental scientific research of the SB RAS I.1.1., project 0314-2016-0004.
Received: 22.12.2016
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 243, Issue 4, Pages 601–611
DOI: https://doi.org/10.1007/s10958-019-04561-x
Bibliographic databases:
Document Type: Article
UDC: 512.54
Language: English
Citation: G. A. Noskov, “Plotkin's geometric equivalence, Mal'cev's closure and incompressible nilpotent groups”, Problems in the theory of representations of algebras and groups. Part 33, Zap. Nauchn. Sem. POMI, 470, POMI, St. Petersburg, 2018, 147–161; J. Math. Sci. (N. Y.), 243:4 (2019), 601–611
Citation in format AMSBIB
\Bibitem{Nos18}
\by G.~A.~Noskov
\paper Plotkin's geometric equivalence, Mal'cev's closure and incompressible nilpotent groups
\inbook Problems in the theory of representations of algebras and groups. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 470
\pages 147--161
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6617}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 243
\issue 4
\pages 601--611
\crossref{https://doi.org/10.1007/s10958-019-04561-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074480495}
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