A Study of Quasigroups, a Computational Approach on Isotopism and Isomorphism Hierarchical Structure

Author

Runaldo Montrose, The University of Texas Rio Grande Valley

Date of Award

7-2025

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Sergey Grigorian

Second Advisor

Timothy Huber

Third Advisor

Brandt Kronholm

Abstract

Quasigroups morphism classification can present a real computational challenge. As of today, the number of quasigroups that can be generated from a finite set S of cardinality n is known for very small value of n. Though we know the number of quasigroups for small n, generating them in real time is a whole other issue that leads to a bigger challenge of building their isomorphy classes, because the algorithm used required large computing memory resources. In this paper we will expose the computational complexity of constructing their hierarchical morphism structure from isotopism to isomorphism. As an improvement, we shall develop and prove a series of mathematical formulas and theorems, that we will use to lower the processing time in such a way that we can even do real time processing for smaller order of n.

Comments

Copyright 2025 Runaldo Montrose. All Rights Reserved. https://proquest.com/docview/3254070559

Recommended Citation

Montrose, R. (2025). A study of quasigroups, a computational approach on isotopism and isomorphism hierarchical structure [Master's thesis, The University of Texas Rio Grande Valley]. ScholarWorks @ UTRGV. https://scholarworks.utrgv.edu/etd/1768