Submission date: 3 March 2009.

Abstract:

Let Γ be a torsion-free hyperbolic group. We show that the set of solutions of any system of equations with one variable in Γ is a finite union of points and cosets of centralizers if and only if any two-generator subgroup of Γ is free.

Mathematics Subject Classification:

Keywords and phrases: One variable equations, torsion-free hyperbolic groups

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