One Variable Equations in Torsion-Free Hyperbolic Groups

2009/02/20 by Houcine, Abderezak Ould
#FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.0902.3599

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.

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