Definable sets in a hyperbolic group

Olga Kharlampovich, Alexei Myasnikov

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We give a description of definable sets P = (p1,...,p m) in a free non-abelian group F and in a torsion-free non-elementary hyperbolic group G. As a corollary we show that proper non-cyclic subgroups of F and G are not definable. This answers Malcev's question posed in 1965 for F.

Original languageEnglish
Pages (from-to)91-110
Number of pages20
JournalInternational Journal of Algebra and Computation
Volume23
Issue number1
StatePublished - Feb 2013

Keywords

  • Free group
  • definable set

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