test words, test elements, endomorphisms, automorphisms, hyperbolic groups
Subject:
20E36, 20F232
Abstract:
We prove that in many, perhaps all, torsion free
hyperbolic groups, test elements are precisely those elements not
contained in proper retracts. We also show that all Fuchsian
groups have this property. Finally, we show that all surface
groups except ${\mathbb Z} \times {\mathbb Z}$ have test elements.