Complex hyperbolic triangle groups of type m, m, 0;n₁, n₂, 2

Abstract In this paper we study discreteness of complex hyperbolic triangle groups of type m, m, 0; n₁, n₂, 2 m, m, 0 ; n 1, n 2, 2, i. e. groups of isometries of the complex hyperbolic plane generated by three complex reflections of orders n₁, n₂, 2 n 1, n 2, 2 in complex geodesics with pairwise distances m, m, 0. For fixed m, the parameter space of such groups is of real dimension one. We determine the possible orders for n₁ n 1 and n₂ n 2 and also intervals in the parameter space that correspond to discrete and non-discrete triangle groups.