Discrete Hyperbolic Transformations as Unique Product Groups

Steven M. Hair

This paper uses the action of groups acting on hyperbolic 2 and 3-space to prove that certain groups are unique product groups. Specifically it is proved that torsion free Fuchsian groups and torsion free subgroups of Picard's group are unique product groups. Though these results can be obtained from the known structure of these groups, it would seem reasonable that the techniques used in this paper will give new examples of unique product groups. (Advisor Peter A. Linnell)