Description of Coordinate Groups of Irreducible Algebraic Sets over Free 2-Nilpotent Groups

Description of Coordinate Groups of Irreducible Algebraic Sets over Free 2-Nilpotent Groups Full article

Journal

Doklady Mathematics
ISSN: 1064-5624 , E-ISSN: 1531-8362

Output data

Year: 2022, Volume: 105, Number: 2, Pages: 68-70 Pages count : 3 DOI: 10.1134/S1064562422020041

Tags

algebraic geometry over groups; algebraic set; coordinate groups; discrimination; irreducible algebraic set; universal equivalence

Authors

Amaglobeli M.G. ¹ , Miasnikov A.G. ² , Remeslennikov V.N. ³

Affiliations

1	Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia
2	Stevens Institute of Technology, Hoboken, United States
3	Omsk Department of the Sobolev Institute of Mathematics, Russian Academy of Sciences, Omsk, Russian Federation

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. © 2022, Pleiades Publishing, Ltd.

Amaglobeli M.G. , Miasnikov A.G. , Remeslennikov V.N.
Description of Coordinate Groups of Irreducible Algebraic Sets over Free 2-Nilpotent Groups
Doklady Mathematics. 2022. V.105. N2. P.68-70. DOI: 10.1134/S1064562422020041 WOS Scopus РИНЦ OpenAlex

Амаглобели М.Г. , Мясников А.Г. , Ремесленников В.Н.
Описание координатных групп неприводимых алгебраических множеств над свободными 2-нильпотентными группами
Доклады Академии наук. Серия: Математика, информатика, процессы управления. 2022. Т.503. №1. С.23-25. DOI: 10.31857/S2686954322020047 РИНЦ

Web of science:	WOS:000825354000004
Scopus:	2-s2.0-85133642781
Elibrary:	49158369
OpenAlex:	W4286652286

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