One Variable Equations in Torsion-Free Hyperbolic Groups

Abderezak Ould Houcine

One Variable Equations in Torsion-Free Hyperbolic Groups

Group Theory 2009-02-23 v2 Logic

Authors: Abderezak Ould Houcine

Abstract

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

group theory hyperbolic groups

Cite

@article{arxiv.0902.3599,
  title  = {One Variable Equations in Torsion-Free Hyperbolic Groups},
  author = {Abderezak Ould Houcine},
  journal= {arXiv preprint arXiv:0902.3599},
  year   = {2009}
}

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