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 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. Author information: John C. O'Neill : DFMS, United States Air Force Academy, CO 80840-6252 John.Oneill@usafa.af.mil http://www.usafa.af.mil/dfms/people/oneill.htm Edward C. Turner : Dept. of Math., University at Albany, Albany, NY 12222 ted@math.albany.edu http://nyjm.albany.edu:8000/~ted