Algorithmic and combinatorial methods for enumerating the relators of a group presentation

TL;DR

This paper introduces an efficient algorithm for enumerating relators in a finite group presentation, significantly improving over classical methods in terms of complexity by leveraging combinatorial and algorithmic techniques.

Contribution

It presents a novel algorithm that computes relators up to given length and area bounds with better complexity than traditional van Kampen diagram methods.

Findings

Algorithm outperforms classical methods in complexity

Efficient enumeration of relators up to specified bounds

Potential applications in computational group theory

Abstract

The main achievement of this thesis is an algorithm which given a finite group presentation and natural numbers n and k, computes all the relators of length and area up to n and k respectively. The complexity of this algorithm is better by a factor which is over-exponential than that of classical methods using van Kampen diagrams.