Generators of the sister of Euclidean Picard modular group

TL;DR

This paper defines the sister of the Euclidean-Picard modular group and determines its generators using a geometric approach, expanding understanding of modular groups related to complex hyperbolic geometry.

Contribution

It introduces a new concept of the sister of the Euclidean-Picard modular group and provides a method to find its generators, which was not previously established.

Findings

Defined the sister of the Euclidean-Picard modular group.

Derived generators for this group using geometric methods.

Extended the framework of modular group analysis.

Abstract

The sister of Eisenstein-Picard modular group was described in [8]. In this paper we give a similar definition of the sister of the Euclidean-Picard modular group and find its generators by using a geometric method.