A characterization of Fuchsian groups in SU (n, 1)

Let be a non-elementary subgroup of . In this paper, we show that if each loxodromic element in is hyperbolic, then is Fuchsian. We also construct two examples, which imply that the condition “each loxodromic element in is hyperbolic” is necessary when and this condition coincides with “ for all ” when .