Unfaithful complex hyperbolic triangle groups, II: Higher order reflections

We consider symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2π/ 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 application we have in mind is that such groups are candidates for nonarithmetic lattices in SU(2, 1).