Algebr Represent Theor (2010) 13:219–230 DOI 10.1007/s10468-008-9116-3 Normal Subgroups of Hecke Groups H (λ) Özden Koruo ˘ glu · Recep Sahin · Sebahattin ˙ Ikikardes · Ismail Naci Cangül Received: 16 January 2008 / Accepted: 27 September 2008 / Published online: 19 February 2009 © Springer Science + Business Media B.V. 2009 Abstract Let λ ≥ 2 and let H(λ) be the Hecke group associated to λ. Also let H(λ)\U be the Riemann surface associated to the Hecke group H(λ). In this article, we study the even subgroup H e (λ) and the power subgroups H m (λ) of the Hecke groups H(λ). We also study some genus 0 normal subgroups of finite index of H(λ). Finally, we discuss free normal subgroups of H(λ). Keywords Hecke group · Even subgroup · Power subgroup · Free normal subgroup Mathematics Subject Classifications (2000) 11F06 · 20H05 · 20H10 1 Introduction The Hecke groups H(λ) are the set of linear fractional transformations generated by T (z) =− 1 z and S(z)= − 1 z + λ , Presented by Alain Verschoren. Ö. Koruo ˘ glu (B ) Necatibey E ˘ gitim Fakültesi, ˙ Ilkö ˘ gretim Matematik Bölümü, Balıkesir Üniversitesi, 10100 Balıkesir, Turkey e-mail: ozdenk@balikesir.edu.tr R. Sahin · S. ˙ Ikikardes Fen-Edebiyat Fakültesi, Matematik Bölümü, Balıkesir Üniversitesi, 10145 Balıkesir, Turkey R. Sahin e-mail: rsahin@balikesir.edu.tr S. ˙ Ikikardes e-mail: skardes@balikesir.edu.tr I. N. Cangül Fen-Edebiyat Fakültesi, Matematik Bölümü, Uludag Üniversitesi, 16059 Bursa, Turkey e-mail: cangul@uludag.edu.tr