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On three generator Möbius groups. (English) Zbl 0839.30048
Gehring and Martin have shown that two-generator Möbius groups in the extended complex plane $$C_\infty$$ are completely determined up to conjugacy by three special trace parameters. The author establishes the corresponding result for three-generator Möbius groups. The author considers six special traces and shows that the groups sharing the same six values fall into at most two conjugacy classes. The construction of the groups corresponding to a given set of values is very explicit. By example the author shows that one of the two classes may consist of discrete groups, the other of indiscrete. The author has similar results when there are more than three generators.
Reviewer: J.W.Cannon (Provo)

##### MSC:
 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
##### Keywords:
Fuchsian groups; Möbius groups; conjugacy