On Multiplication Groups of Quasigroups

<p>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.</p>

Name thesis:degree_name

Mathematics, PhD

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

Institute of Mathematical Sciences

Year dc:date.available

2022

Author dc:creator

• Al Fares, Ahmed

Contributors dc:contributor

• Lenny Fukshansky
• Ali Nadim
• Michael Orrison

• groups
• Latin squares
• loops
• multiplication groups
• quasigroups
• roots of unity
• Mathematics

Repository record dc:identifier

https://scholarship.claremont.edu/cgu_etd/475

OAI identifier oai:identifier

oai:scholarship.claremont.edu:cgu_etd-1506