On the extended Hecke group (H)over-bar (lambda(5))

Abstract

We consider the extended Hecke group (H) over bar(gimel(5)) generated by T(z) = -1/z, S(z) = -1/(z + gimel(5)) and R(z) = 1/(z) over bar with gimel(5) = 2cos(pi/5) = (1 + root 5)/2. In this paper, we study the abstract group structure of the extended Hecke group and its power subgroups (H) over bar (m)(gimel(5)). Also, we give relations between power subgroups and commutator subgroups of the extended Hecke group (H) over bar(gimel 5).