One Variable Equations in Torsion-Free Hyperbolic Groups

Details One Variable Equations in Torsion-Free Hyperbolic Groups One Variable Equations in Torsion-Free Hyperbolic Groups

2009-02-20

arxiv.org/abs/0902.3599v2

Mathematics

Group Theory

Scientific paper

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.

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