## One Variable Equations in Torsion-Free Hyperbolic Groups

##### Authors
Houcine, Abderezak Ould
##### Description
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