Test Elements and the Retract Theorem in Hyperbolic Groups

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.

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