The chordal norm of discrete Mobius groups in several dimensions

Let d(f, g) = sup{d(f(z),g(z)) : z epsilon (C) over bar} where f, g are Mobius transformations and d(z(1),z(2)) denotes the chordal distance between z(1), z(2) in (C) over bar. We show that if (f,g) is a discrete group and if fg not equal gf, then max{d(f, id), d(g, id)} greater than or equal to c where .863 less than or equal to c less than or equal to .911... We also obtain some higher dimensional analogs by means of Clifford numbers.