Discriminating completions of hyperbolic groups

Gilbert Baumslag, Alexei Myasnikov, Vladimir Remeslennikov

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

A group G is called an A-group, where A is a given Abelian group, if it comes equipped with an action of A on G which mimics the way in which Z acts on any group. This action is codified in terms of certain axioms, all but one of which were introduced some years ago by R. C. Lyndon. For every such G and A there exists an A-exponential group GA which is the A-completion of G. We prove here that if G is a torsion-free hyperbolic group and if A is a torsion-free Abelian group, then the Lyndon's type completion GA of G is G-discriminated by G. This implies various model-theoretic and algorithmic results about GA.

Original languageEnglish
Pages (from-to)115-143
Number of pages29
JournalGeometriae Dedicata
Volume92
Issue number1
DOIs
StatePublished - 2002

Keywords

  • Algebraic geometry over groups
  • Completions
  • Discrimination
  • Hyperbolic groups

Fingerprint

Dive into the research topics of 'Discriminating completions of hyperbolic groups'. Together they form a unique fingerprint.

Cite this