Trace classes and fixed points for the extended modular group $\overline\Gamma$

Abstract

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