Jøorgensens famous inequality gives a necessary condition for a subgroup of PSL(2,) to be discrete. It is also true that if Jrgensens inequality holds for every nonelementary two-generator subgroup, the group is discrete. The sufficient condition has been generalized to many settings. In this paper, we continue the work of Wang, Li and Cao (Discreteness criteria for Möbius groups acting on ℝ̄n II, Israel J. Math. 150 (2005), 357-368) and find three more (infinite) discreteness criteria for groups acting on ℝ̄n II; we also correct a lingui...
