Trace classes and fixed points for the extended modular group $overlineGamma$

Abstract

The extended modular group $overlineGamma$ = PGL(2,$Bbb{Z}$) is the group obtained by adding the reflection R(z) = 1/$overline z$ to the generators of the modular group $overlineGamma$ = PSL(2,$Bbb{Z}$). In this paper, we find the trace classes of the extended modular group $overlineGamma$. Using this, we classify the elements of $overlineGamma$.