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Inequalities in discrete subgroups of PSL(2,$ℝ\right)$. (English) Zbl 0629.20023
We find necessary and sufficient conditions for a non-elementary subgroup, F, of PSL(2,$ℝ\right)$ to be discrete. The conditions are that for each pair of hyperbolic elements in F one of three inequalities in their multipliers and their cross ratio is satisfied. Unlike many results in this area, the inequalities are independent of any normalizations and thus may be more useful.
##### MSC:
 20H10 Fuchsian groups and their generalizations (group theory) 20F05 Generators, relations, and presentations of groups