Some Normal Subgroups of Extended Generalized Hecke Groups

Abstract

Generalized Hecke group H p,∞ (λ) is generated by X(z) = −(z − λ p ) −1 and Y (z) = −(z + λ) −1 where λ p = 2 cos πp , p ≥ 2 integer and λ ≥ 2 . Extended generalized Hecke group H p,∞ (λ) is obtained by adding the reection R(z) = 1/z to the generators of generalized Hecke group H p,∞ (λ). In this paper, we study the commutator subgroups of ex- tended generalized Hecke groups H p,∞ (λ). Also, we determine the power subgroups of generalized Hecke groups H p,∞ (λ) and extended generalized Hecke groups H p,∞ (λ) .