Limits of relatively hyperbolic groups and Lyndon's completions

Olga Kharlampovich, Alexei Myasnikov

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We describe finitely generated groups H universally equivalent (with constants from G in the language) to a given torsion-free relatively hyperbolic group G with free abelian parabolics. It turns out that, as in the free group case, the group H embeds into Lyndon's completion G ℤ[t ] of the group G, or, equivalently, H embeds into a group obtained from G by finitely many extensions of centralizers. Conversely, every subgroup of G ℤ[t ] containing G is universally equivalent to G. Since finitely generated groups universally equivalent to G are precisely the finitely generated groups discriminated by G, the result above gives a description of finitely generated groups discriminated by G. Moreover, these groups are exactly the coordinate groups of irreducible algebraic sets over G.

Original languageEnglish
Pages (from-to)659-680
Number of pages22
JournalJournal of the European Mathematical Society
Volume14
Issue number3
DOIs
StatePublished - 2012

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