MATH337: GROUPS — PRESENTATIONS AND REPRESENTATIONS

(Other mathematical websites by Dr C.D.H. Cooper www.maths.mq.edu.au/~chris)

 

Introduction and Table of Contents

http://www.ics.mq.edu.au/~chris/math337/intro.pdf

 

Chapter 1: Introduction to Groups

http://www.ics.mq.edu.au/~chris/math337/chap01.pdf

 

Chapter 2: Permutations

http://www.ics.mq.edu.au/~chris/math337/chap02.pdf

 

Chapter 3: Examples of Groups

http://www.ics.mq.edu.au/~chris/math337/chap03.pdf

 

Chapter 4: First Steps in the Theory

http://www.ics.mq.edu.au/~chris/math337/chap04.pdf

 

Chapter 5: The Todd-Coxeter Algorithm (updated 15th April 2005)

http://www.ics.mq.edu.au/~chris/math337/chap05.pdf

 

Chapter 6: A Second Round of Theory

http://www.ics.mq.edu.au/~chris/math337/chap06.pdf

 

Chapter 7: Representations of Finite Groups

http://www.ics.mq.edu.au/~chris/math337/chap07.pdf

 

Chapter 8: Groups Acting on Sets

http://www.ics.mq.edu.au/~chris/math337/chap08.pdf

 

Chapter 9: Free Groups

http://www.ics.mq.edu.au/~chris/math337/chap09.pdf

 

Chapter 10: Soluble Groups

http://www.ics.mq.edu.au/~chris/math337/chap10.pdf

 

Chapter 11: Finitely Generated Abelian Groups (updated 20th May 2005)

http://www.ics.mq.edu.au/~chris/math337/chap11.pdf

 

Chapter 12: Infinite Abelian Groups

http://www.ics.mq.edu.au/~chris/math337/chap12.pdf

 

APPENDICES   http://www.ics.mq.edu.au/~chris/math337/appendix.pdf

Appendix A: Groups of Small Order

Appendix B: Character Table Summary

Appendix C: A Group of Order 12

This goes through the many steps, with a group of order 12, that students in MATH337 are required to do with their project group of order 16.  It is therefore a useful guide for completing this project.

Appendix D: Group Presentations for Groups of Order 16

 

NOTES ON GROUPOIDS AND FREE GROUPS

These are based on notes prepared by Professor Ross Street as an alternative to chapter 9.

http://www.ics.mq.edu.au/~chris/math337/chap13.pdf

http://www.ics.mq.edu.au/~chris/math337/chap14.pdf