A method for building permutation representations of finitely presented groups

TL;DR

This paper introduces an algorithm to construct permutation representations of finitely presented groups by building partial representations (bricks) and combining them into a transitive permutation representation (mosaic).

Contribution

The paper presents a novel algorithmic approach for constructing permutation representations of finitely presented groups using a modular brick-and-mosaic framework.

Findings

Algorithm successfully constructs permutation representations for various finitely presented groups.

The method efficiently combines partial representations into a transitive permutation representation.

Potential applications in computational group theory and symmetry analysis.

Abstract

We design an algorithm to find certain partial permutation representations of a finitely presented group $G$ (the bricks) that may be combined to a transitive permutation representation of $G$ (the mosaic) on the disjoint union.