Date of Award

Fall 11-21-2025

Document Type

Dissertation

Degree Name

Ph.D. in Mathematics

Organizational Unit

College of Natural Science and Mathematics, Mathematics

First Advisor

Petr Vojtechovsky

Second Advisor

Mandi A. Schaeffer Fry

Third Advisor

Michael Kinyon

Fourth Advisor

J. Michael Daniels

Copyright Statement / License for Reuse

All Rights Reserved
All Rights Reserved.

Keywords

Algebra, Knot theory, Nonassociative, Quandles

Abstract

This thesis concerns principal quandles and, as a special case, Alexander quandles. A principal quandle is a coset quandle, Q(G,H, f), in which the subgroup H is trivial. If in addition the group G is abelian, then the coset quandle is called an Alexander quandle. The isomorphism types of Alexander quandles were classified [16], and some progress was made on describing the isomorphism types of principal quandles in [14] and [13]. The first part of this thesis applies the ideas used in Holmes’ paper to give a classification of the isomorphism types of principal quandles. The second part of the thesis follows the work of Hou in [17]; focusing on Λ-modules and their use in constructing Alexander quandles of order pn.

Copyright Date

11-2025

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance.

Rights Holder

Jesse Parrish

Provenance

Received from ProQuest

File Format

application/pdf

Language

English (eng)

Extent

136 pgs

File Size

8.2 MB

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