Date of Award

Spring 2021

Document Type


Degree Name

Master of Arts (MA)



Committee Chairperson

Shiv Gupta, Ph.D.

Committee Member

Jeremy Brazas, Ph.D.

Committee Member

Michael Fisher, Ph.D.


This thesis gives an introduction to some topics from group theory, with a focus on automorphism groups of finite groups. Chapter one introduces the basic definitions and properties of groups and subgroups. In chapter two, the different classifications of functions between groups are defined and some properties thereof are given. Here we define automorphisms which are the focus of the paper. Chapters three and four deal with permutation groups and Sylow theorems respectively, and are discussions of some important groups, subgroups, and theorems pertaining thereto. The topics of these chapters help with our discussion of automorphism groups in the final three chapters. Chapter five gives a discussion on the automorphism groups of finite groups of small order, and then some general results about the automorphism groups of cyclic groups. The last two chapters are dedicated to interesting case studies in the study of automorphism groups. Chapter six discusses an example of a group G which has an outer automorphism which preserves the conjugate classes of a group, and chapter seven gives the introduction and details to the theorem that S_6 is the only symmetric group having an outer automorphism.

Included in

Algebra Commons