a1 The University, Southampton
Let denote the group of transformations of the upper-half complex plane U onto itself of the form
If, on U, we introduce the Riemannian metric ds = |dz| y−1 (z = x + iy), then U becomes a model of the hyperbolic plane and its group of isometries. The set of elements of type I, the orientation-preserving isometries form a subgroup of index two in , which we denote by .
(Received May 12 1972)