The Distant Graph of the Ring of Integers and Its Representations in the Modular Group

摘要

There is presented an infinite class of subgroups of the modular group PSL(2, Z) that serve as Cayley representations of the distant graph of the projective line of integers. They are infinite countable free products of subgroups of PSL(2, Z) isomorphic with Z(2), Z(3) and Z subject to the restriction that the number of copies of Z is 0 or 2. The proof technique is based on a 1-1 correspondence between some involutions. of Z that fulfill the equation