Abikoff, William; Haas, Andrew Nondiscrete groups of hyperbolic motions. (English) Zbl 0709.20026 Bull. Lond. Math. Soc. 22, No. 3, 233-238 (1990). 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 Cited in 1 ReviewCited in 15 Documents MSC: 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 Keywords:group of hyperbolic isometries; two-generator subgroups; discreteness Citations:Zbl 0698.20037 PDFBibTeX XMLCite \textit{W. Abikoff} and \textit{A. Haas}, Bull. Lond. Math. Soc. 22, No. 3, 233--238 (1990; Zbl 0709.20026) Full Text: DOI