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John C. O'Neill and Edward C. Turner
Test Elements and the Retract Theorem in Hyperbolic Groups
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| Published: |
July 21, 2000 |
| Keywords: |
test words, test elements, endomorphisms, automorphisms, hyperbolic groups |
| Subject: |
20E36, 20F232 |
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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 Z×Z have test elements.
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| 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
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