MATH337 Groups: Presentations and Representations

This is a first course on group theory but is more suitable to a third year student than a first year one.

Groups It attempts to motivate group theory with many illustrative examples such as shuffling of cards, bell ringing and permutation puzzles.

As well as the usual introductory theory there’s an elementary introduction to representation theory, to the Todd-Coxeter algorithm and to free groups.

[Please note that all links are to Adobe .pdf documents. They will open in a separate browser window.]

Introduction and Table of Contents
Chapter 1: Introduction to Groups
Chapter 2: Permutations
Chapter 3: Examples of Groups
Chapter 4: First Steps in the Theory
Chapter 5: The Todd-Coxeter Algorithm
Chapter 6: A Second Round of Theory
Chapter 7: Representations of Finite Groups
Chapter 8: Groups Acting on Sets
Chapter 9: Free Groups
Chapter 10: Finitely Generated Abelian Groups
Chapter 11: Soluble Groups
Chapter 12: Infinite Abelian Groups
Appendices

Appendix A: Groups of Small Order
Appendix B: Character Table Summary
Appendix C: A Group of Order 12
Appendix D: Group Presentations for Groups of Order 16