Year: 2025
Type: article
Abstract: This paper transforms the triviality search problem in group presentations into an optimization problem by defining decision variables, objective functions, and constraints, and conducts an in-depth analysis of the scale and complexity of the proposed model, highlighting its computational challenges. A genetic algorithm-based solution framework is designed to efficiently search for Andrews-Curtis transformation sequences, and its effectiveness for specific group presentations is validated, successfully solving the Andrews-Curtis transformation sequence search problem. This study not only provides a novel methodology for addressing the triviality search problem but also demonstrates the practical application of optimization techniques in group theory, offering new insights for future research in this field.
Author: <p>Yifeng Wei</p>
Institution: China Jiliang University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W4412920140