Power subgroups of the extended hecke groups

Abstract

We 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 >= 3 integer: In this article, we study the abstract group structures of the power subgroups (H) over bar (m) (lambda(q)) of (H) over bar (lambda(q)) for each positive integer m. Then, we give the relations between commutator subgroups and power subgroups.