On the Subgroups of the Extended Hecke, Hecke and Picard Groups

TL;DR

This paper investigates the low index subgroups of the extended Hecke, Hecke, Picard, and modular groups using color symmetry theory, providing a comprehensive classification of these subgroups.

Contribution

It introduces a novel application of color symmetry theory to derive low index subgroups of these important groups.

Findings

Classified low index subgroups of the extended Hecke, Hecke, and Picard groups.

Presented the low index subgroups of the modular group.

Enhanced understanding of subgroup structures in these groups.

Abstract

In this work, we derive the low index subgroups of the extended Hecke, Hecke and the Picard groups using tools in color symmetry theory. We also present the low index subgroups of the modular group.