On the distance between the axes of elliptic elements generating a free product of cyclic groups

摘要

Let f and g be elliptic Mobius transformations of respective orders m ≥ 3, n ≥ 2, and let s, φ be the hyperbolic distance and angle between their axes. In this paper we prove that for cosh s≥ 1+cosπ/mcosπcosφ/sinπ/msinπ the group is discrete, nonelementary and isomorphic to the free product of cyclic groups. Several examples are given showing the effectiveness of the above estimate for cosh s.