Nondiscrete groups of hyperbolic motions. (English) Zbl 0709.20026

It is proved that a nonelementary n-dimensional group of hyperbolic isometries is discrete if and only if each of its two-generator subgroups is discrete. When n is even, discreteness follows from that of the cyclic subgroups. These results have also been obtained by G. Martin [Acta Math. 163, No.3/4, 253-289 (1989; Zbl 0698.20037)].
Reviewer: T.Jørgensen


20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
11F06 Structure of modular groups and generalizations; arithmetic groups


Zbl 0698.20037
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