Date of Award

December 2012

Degree Type


Degree Name

Master of Science



First Advisor

Jeb F. Willenbring

Committee Members

Jeb F. Willenbring, Yi Ming Zou, Gabriella Pinter


Class Equation, Conjugacy Classes, General Linear Group


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.

Included in

Mathematics Commons