Date of Award
Fall 2022
Degree Type
Open Access Dissertation
Degree Name
Mathematics, PhD
Program
Institute of Mathematical Sciences
Advisor/Supervisor/Committee Chair
Gizem Karaali
Dissertation or Thesis Committee Member
Lenny Fukshansky
Dissertation or Thesis Committee Member
Ali Nadim
Dissertation or Thesis Committee Member
Michael Orrison
Terms of Use & License Information
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Rights Information
© 2022 Ahmed Al Fares
Keywords
groups, Latin squares, loops, multiplication groups, quasigroups, roots of unity
Subject Categories
Mathematics
Abstract
Quasigroups are algebraic structures in which divisibility is always defined. In this thesis we investigate quasigroups using a group-theoretic approach. We first construct a family of quasigroups which behave in a group-like fashion. We then focus on the multiplication groups of quasigroups, which have first appeared in the work of A. A. Albert. These permutation groups allow us to study quasigroups using group theory. We also explore how certain natural operations on quasigroups affect the associated multiplication groups. Along the way we take the time and special care to pose specific questions that may lead to further work in the near future.
ISBN
9798845410566
Recommended Citation
Al Fares, Ahmed. (2022). On Multiplication Groups of Quasigroups. CGU Theses & Dissertations, 475. https://scholarship.claremont.edu/cgu_etd/475.
