Discreteness criterions of isometric subgroups for quaternionic hyperbolic space. (Q1771163)

The author gives an analogue of Jørgensen's inequality for non-elementary groups of isometries of complex hyperbolic 2-space generated by two elements, one is either loxodromic or boundary elliptic for the same group of isometries of quaternionic hyperbolic 2-space. This is an ex-problem regarding two generator discrete groups since Jørgensen's inequality was given in 1970. He gives a sufficient condition for a non-elementary subgroup of isometries of quaternionic hyperbolic 2-space generated by two elements one of which is parabolic not to be discrete.