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Limits of relatively hyperbolic groups and Lyndon’s completions

By Olga Kharlampovich and Alexei Myasnikov


In this paper 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 the 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 finitel

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Year: 2009
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