#### Date of Award

December 2012

#### Degree Type

Thesis

#### Degree Name

Master of Science

#### Department

Mathematics

#### First Advisor

Jeb F. Willenbring

#### Committee Members

Jeb F. Willenbring, Yi Ming Zou, Gabriella Pinter

#### Keywords

Class Equation, Conjugacy Classes, General Linear Group

#### Abstract

In this thesis, we discuss the conjugacy classes of the general linear group of 2 x 2 matrices over a prime field. We find the number of conjugacy classes and the class equation for GL_2 (F_q) for general prime q. We then look at some applications of the class equation, which includes finding the number of orbits when GL_2 (F_q) acts on (GL_2 (F_q))^s by conjugation. Included in this thesis is the Maple Code for generating the class equation for any prime.

#### Recommended Citation

Mathewson, Lindsey, "The Class Equation of GL2(Fq)" (2012). *Theses and Dissertations.* Paper 37.

http://dc.uwm.edu/etd/37