On the extended hecke groups H¯¯¯¯¯(λq)

Abstract

Hecke groups H(λq) have been studied extensively for many aspects in the literature, [5], [8]. The Hecke group H(λ3), the modular group PSL(2,Z ) , has especially been of great interest in many fields of mathematics, for example number theory, automorphic function theory and group theory. In this paper we consider the extended Hecke groups H¯¯¯¯¯(λq) which are defined analogously with the extended modular group. We find the conjugacy classes of torsion elements in H¯¯¯¯¯(λq). Using this we give some results about the normal subgroups and Fuchsian subgroups of H¯¯¯¯¯(λq).