A class of congruence subgroups of hecke group H ( λ 5)

Abstract

In [2], it is shown that, for some Hecke groups, unlike the modular group, two definitions of the principal congruence subgroups may not coincide and congruence and principal congruence subgroups of two important Hecke groups H (SICm), for m = 2 or 3, are classified and the quotients of H (SICm) with these normal subgroups are given. Here we obtain a classification of the congruence subgroups obtained as the kernel of reduction homomorphism for another important Hecke group H (lambda(5)) and also obtain the quotient groups. Finally the indices and abstract group structure of all these subgroups are determined.