Trace classes and fixed points for the extended modular group Γ

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 $\overline\Gamma$.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 $\overline\Gamma$.