Geometric equivalence of π-torsion-free nilpotent groups

R. Lipyanski

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Abstract

In this paper, we study the notion of geometric equivalence of groups introduced by B. Plotkin [P1, P2]. Sufficient and necessary conditions are presented for a π-torsion-free nilpotent group to be geometrically equivalent to its π-completion. We prove that a relatively free nilpotent π-torsion-free group and its π-completion define the same quasi-variety. Examples of π-torsion-free nilpotent groups that are geometrically equivalent to their π-completions are given.

Original languageEnglish
Title of host publicationGroups, Algebras and Identities
EditorsEugene Plotkin
PublisherAmerican Mathematical Society
Pages123-133
Number of pages11
ISBN (Print)9781470437138
DOIs
StatePublished - 1 Jan 2019
EventResearch Workshop of the Israel Science Foundation on Groups, Algebras and Identities, 2016 - Jerusalem, Israel
Duration: 20 Mar 201624 Mar 2016

Publication series

NameContemporary Mathematics
Volume726
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Conference

ConferenceResearch Workshop of the Israel Science Foundation on Groups, Algebras and Identities, 2016
Country/TerritoryIsrael
CityJerusalem
Period20/03/1624/03/16

Keywords

  • Geometric equivalence
  • Nilpotent groups
  • Q-powered groups

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