Arithmeticity of orbifold generalised triangle groups

Abstract

Maclachlan and Martin have proved that only finitely many arithmetic Kleinian groups can be generated by 2 elliptic elements, and have classified these groups in the non-cocompact case. Here, we investigate the cocompact case, restricting to a class of generalised triangle groups considered by Jones and Reid which arise as the fundamental groups of hyperbolic 3-dimensional orbifolds. We obtain 21 arithmetic groups and provide a description of the corresponding orbifolds.