Some Results On Homomorphic Images of ∆(2, 3, 13)

Abstract

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