Date of Award

5-2023

Document Type

Thesis

Degree Name

Bachelor of Science

Department

Math & Statistics

First Advisor

Dr. Jim Davis

Abstract

In this work, we investigate the structure of particular partial difference sets (PDS) of size 70 with Denniston parameters in an elementary abelian group and in a nonelementary abelian group. We will make extensive use of character theory in our investigation and ultimately seek to understand the nature of difference sets with these parameters. To begin, we will cover some basic definitions and examples of difference sets and partial difference sets. We will then move on to some basic theorems about partial difference sets before introducing a group ring formalism and using it to explore several important constructions of partial difference sets. Finally, we will conclude our introduction by developing the character theory that we will exploit to understand our partial difference sets.

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