Some subgroups of the extended Hecke groups H(-)over-bar(lambda(q))

Abstract

The authors consider the extended Hecke groups (H) over bar(lambda(q)) generated by T(z) = -1/z, S(z) = -1/(z + lambda(q)) and R(z) = 1/(z) over bar with lambda(q) = 2 cos(pi/q) for q greater than or equal to 3 an integer. In this paper, the even subgroup (H) over bar (e)(lambda(q)), the second commutator subgroup (H) over bar "(lambda(q)) and the principal congruence subgroups (H) over bar (p)(lambda(q)) of the extended Hecke groups (H) over bar "(lambda(q)) are studied. Also, relations between them are given.