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 $overline{H}(lambda_q)$.