Some normal subgroups of extended generalized Hecke groups

Abstract

Generalized Hecke group H-p,H-infinity (lambda) is generated by X(z) = -(z - lambda(p))(-1) and Y(z) = -(z + lambda)(-1) where lambda(p) = 2 cos pi/p, p >= 2 integer and lambda >= 2. Extended generalized Hecke group (H) over bar (p,infinity) (lambda) is obtained by adding the reflection R(z) = 1/(z) over bar to the generators of generalized [lecke group H-p,H-infinity(lambda). In this paper, we study the commutator subgroups of extended generalized [lecke groups (H) over bar (p,infinity) (lambda). Also, we determine the power subgroups of generalized Hecke groups H-p,H-infinity(lambda) and extended generalized Hecke groups (H) over bar (p,infinity)(lambda).