On Normal Subgroups of Generalized Hecke Groups

We consider the generalized Hecke groups H_p,q generated by X(z) = -(z -λ_p)^-1, Y (z) = -(z +λ_q)^-1 with and where 2 ≤ p ≤ q < ∞, p+q > 4. In this work we study the structure of genus 0 normal subgroups of generalized Hecke groups. We construct an interesting genus 0 subgroup called even subgroup, denoted by . We state the relation between commutator subgroup H′_p,q of H_p,q defined in [1] and the even subgroup. Then we extend this result to extended generalized Hecke groups H̅_p,q.