Some normal subgroups of the extended Hecke groups H(lambda(p))

Abstract

We consider the extended Hecke groups (H) over bar (lambda p) generated by T(z) = -1/z, S(z) = -1/(z+lambda p) and R(z) = 1/(z) over bar with lambda P = 2 cos(pi/p) for p >= 3 prime number. In this article, we study the abstract group structure of the extended Hecke groups and the power subgroups (H) over bar-(lambda(p)) of (H) over bar(lambda p). Then, we give the relations between commutator subgroups and power subgroups and also the information of interest about free normal subgroups of the extended Hecke groups.