One Variable Equations in Torsion-Free Hyperbolic Groups

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Houcine, Abderezak Ould
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Abstract
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Let $\Gamma$ be a torsion-free hyperbolic group. We show that the set of solutions of any system of equations with one variable in $\Gamma$ is a finite union of points and cosets of centralizers if and only if any two-generator subgroup of $\Gamma$ is free.
Keywords
Mathematics - Group Theory, Mathematics - Logic
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