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On The Extended Hecke Groups \Overline{H}(\Lambda _Q), Ni̇hal Yilmaz Özgür, Recep Şahi̇n

Turkish Journal of Mathematics

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).