Trace classes and fixed points for the extended modular group (Gamma)over-bar

Abstract

The extended modular group (Gamma) over bar = PGL(2, Z) is the group obtained by adding the reflection R(z) = 1/(z) over bar to the generators of the modular group F = PSL(2, Z). In this paper, we find the trace classes of the extended modular group (Gamma) over bar. Using this, we classify the elements of (Gamma) over bar.