New York Journal of Mathematics
New York J Math
Test Elements and the Retract Theorem in
Hyp erb olic Groups
John C O Neill and Edward C Turner
Abstract We prove that in many p erhaps all torsion free hyp erb olic groups
test elements are precisely those elements not contained in prop er retracts We
also show that all Fuchsian groups have this prop erty Finally weshow that
all surface groups except Z Z have test elements
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