On the Power Subgroups of the Extended Modular Group

Abstract

In this paper we describe the group structure of power subgroups $\overline{\Gamma}^m$ of the extended modular group $\overline{\Gamma}$ and the quotients to them. Then we give some relations between the power subgroups $\overline{\Gamma}^m$, the commutator subgroups $\overline{\Gamma}^\prime$ and $\overline{\Gamma}^{\prime\prime}$ and also the information of interest about free normal subgroups of the extended modular group $\overline{\Gamma}$.