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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 503, Pages 23–25
DOI: https://doi.org/10.31857/S2686954322020047
(Mi danma242)
 

MATHEMATICS

Description of coordinate groups of irreducible algebraic sets over free 2-nilpotent groups

M. G. Amaglobelia, A. G. Myasnikovb, V. N. Remeslennikovc

a Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia
b Stevens Institute of Technology, Hoboken, USA
c Omsk Department of the Sobolev Institute of Mathematics, Russian Academy of Sciences, Omsk, Russia
References:
Abstract: A convenient pure algebraic description of the coordinate groups of irreducible algebraic sets over a non-Abelian free 2-nilpotent group $N$ of finite rank is given. Note that, in algebraic geometry over an arbitrary group $N$, it is natural to consider groups containing $N$ as a subgroup (so-called $N$-groups) and homomorphisms of $N$-groups which are identical on $N$ ($N$-homomorphisms). As a corollary, we describe all finitely generated groups $H$ that are universally equivalent to $N$ (with constants from $N$ in the language). Additionally, we give a pure algebraic criterion determining when a finitely generated $N$-group $H$ that is $N$-separated by $N$ is, in fact, $N$-discriminated by $N$.
Keywords: algebraic geometry over groups, algebraic set, irreducible algebraic set, coordinate groups, discrimination, universal equivalence.
Presented: Yu. L. Ershov
Received: 03.12.2021
Revised: 03.12.2021
Accepted: 23.01.2022
English version:
Doklady Mathematics, 2022, Volume 105, Issue 2, Pages 68–70
DOI: https://doi.org/10.1134/S1064562422020041
Bibliographic databases:
Document Type: Article
UDC: 512.544.33
Language: Russian
Citation: M. G. Amaglobeli, A. G. Myasnikov, V. N. Remeslennikov, “Description of coordinate groups of irreducible algebraic sets over free 2-nilpotent groups”, Dokl. RAN. Math. Inf. Proc. Upr., 503 (2022), 23–25; Dokl. Math., 105:2 (2022), 68–70
Citation in format AMSBIB
\Bibitem{AmaMyaRem22}
\by M.~G.~Amaglobeli, A.~G.~Myasnikov, V.~N.~Remeslennikov
\paper Description of coordinate groups of irreducible algebraic sets over free 2-nilpotent groups
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 503
\pages 23--25
\mathnet{http://mi.mathnet.ru/danma242}
\crossref{https://doi.org/10.31857/S2686954322020047}
\elib{https://elibrary.ru/item.asp?id=48506196}
\transl
\jour Dokl. Math.
\yr 2022
\vol 105
\issue 2
\pages 68--70
\crossref{https://doi.org/10.1134/S1064562422020041}
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