Commutator Subgroups of Generalized Hecke and Extended Generalized Hecke Groups

Let p and q be integers such that 2 ≤ p ≤ q; p + q > 4 and let Hp,q be the generalized Hecke group associated to p and q: The generalized Hecke group Hp,q is generated by X(z) = -(z-λp)-1 and Y (z) = -(z+ λq)-1 where λp = 2 cos ≤ π/p and λq = 2 cos π/q. The extended generalized Hecke group H̅p,q is obtained by adding the reection R(z) = 1/z̅ to the generators of generalized Hecke group Hp,q: In this paper, we study the commutator subgroups of generalized Hecke groups Hp,q and extended generalized Hecke groups H̅p,q.

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