Ž . Splitting Groups of Signature

Let G be a co-compact Fuchsian group. As such, it acts discontinuously on the hyperbolic plane H and the quotient is a closed hyperbolic 2-orbifold. The structure theory for co-compact Fuchsian groups yields a canonical presentation for such groups. This information is described by the signature s s g ; m , . . . , m 1 Ž . Ž . 1 r where g is the genus of the base surface of the quotient 2-orbifold, and the conjugacy classes of the maximal non-trivial finite cyclic subgroups have orders m , . . . , m . In the case when g is zero we will abbreviate the 1 r Ž . signature to m , m , . . . , m . 1 2 r