Unfaithful complex hyperbolic triangle groups

We consider symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2pi / p, with p> 3. We restrict our attention to those groups where certain words are elliptic. Our goal is to find necessary conditions for such a group to be discrete. The main applica-tion we have in mind is that such groups are candidates for nonarithmetic lattices in SU(2, 1). 1