Abstract
It is known that conjugacy classes of actions of PGL (2, Z) on PL(F-q) can be represented by coset diagrams D(theta, q), where theta is an element of F-q and q is a power of a prime p. In this paper, we have obtained conditions in terms of theta and q which ensure the emergence of coset diagrams representing homomorphic images of infinite triangle group Delta(2, 3, 13) =< x, y : x(2) = y(3) = (xy)(13) = 1 > on PL(F-q). We have also found conditions for existence of some special types of fragments in the coset diagrams representing homomorphic images of Delta(2, 3, 13). We have used technique devised in [7] to stitch together small coset diagrams representing homomorphic images of Delta(2, 3, 13) to obtain homomorphic images of the same triangle group but of larger size.