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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 470, Pages 147–161
(Mi znsl6617)
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Plotkin's geometric equivalence, Mal'cev's closure and incompressible nilpotent groups
G. A. Noskov Sobolev Institute of Mathematics, 644043 Omsk, Russia
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.
Received: 22.12.2016
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
Linking options:
https://www.mathnet.ru/eng/znsl6617 https://www.mathnet.ru/eng/znsl/v470/p147
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Abstract page: | 82 | Full-text PDF : | 35 | References: | 19 |
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