Complex hyperbolic triangle groups with 2-fold symmetry

In this paper we will consider the 2-fold symmetric complex hy­perbolic triangle groups generated by three complex reflections through angle 2Π/p with p ≥ 2. We will mainly concentrate on the groups where some ele­ments are elliptic of finite order. Then we will classify all such groups which are candidates for being discrete. There are only 4 types.