On the extended hecke groups $\overline{H}(\lambda q)$

Abstract

Hecke groups $H(\\lambda_q)$ have been studied extensively for many aspects in the literature, [5], [8]. The Hecke group $H(\\lambda_3)$, the modular group PSL(2,$ \\Bbb {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 $\\overline{H}(\\lambda_q)$ which are defined analogously with the extended modular group. We find the conjugacy classes of torsion elements in $\\overline{H}(\\lambda_q)$. Using this we give some results about the normal subgroups and Fuchsian subgroups of $\\overline{H}(\\lambda_q)$.