The normal subgroup structure of the extended Hecke groups

Abstract

We consider the extended Hecke groups (H) over bar(lambda) generated by T (z) = -1/z, S(z) = -1/(z + lambda) and R(z) = 1/(z) over bar with lambda >= 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups (H) over bar(lambda). Then, we determine the abstract group structure of the commutator subgroups (H) over bar' (lambda), the even subgroup (H) over bar (e)(lambda), and the power subgroups (H) over bar (m)(lambda) of the extended Hecke groups (H) over bar(lambda). Also, finally, we give some relations between them.