Petrie Paths in Triangular Normalizer Maps

Abstract

This study is devoted to investigate the Petrie paths in normalizer maps and the regular triangular maps corresponding to the subgroups $\Gamma_0(N)$ of the modular group $\Gamma$. We show that each regular triangular map admits a closed Petrie path. Thus, for each regular map, we find the Petrie length of the corresponding map.