On Normal Subgroups of Generalized Hecke Groups

Abstract

We consider the generalized Hecke groups Hp,q generated by X(z) = -(z -λp)-1, Y (z) = -(z +λq)-1 with and where 2 ≤ 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 Hp,q defined in [1] and the even subgroup. Then we extend this result to extended generalized Hecke groups H̅p,q.

Keywords

• generalized hecke groups
• extended generalized hecke groups
• genus 0 normal subgroups
• even subgroups
• 20h10
• 11f06
• 30f35