## Mathematics 751: Further Group Theory (Honours)

## Semester 1, 2008

**Lecturer: Professor J Moori (Office: F9) moori@ukzn.ac.za**

**
****Mondays: 10:00 - 11:30 (F26); Wednesdays: 10:00 - 11:30 (F26)**

**
Young men should prove theorems, old men should write books. Godfrey H. Hardy,
(1877 - 1947) **

**
Quoted by Freeman Dyson in Freeman Dyson: Mathematician, Physicist, and Writer.
Interview with Donald J. Albers, The College Mathematics Journal, vol. 25, No.
1, January 1994. **

**Content**: This is a further course in GroupTheory
which covers topics on:

- Groups of Small Order
- Permutation Groups and Simplicity of An
- Permutation Representations
- p-Groups and Sylow Theorems
- Normal Series and Soluble Groups
- Fundamental Theorem of Abelian Groups
- Some Examples of Simple Groups
- Representation Theory (Basic Concepts and Characters of Finite Groups)

**Assessment**: 33% [Class mark based on
theoretical and computational assignments] , 67% [3 hour final examination]

**References: **

- An Introduction to the Theory of Groups, J J Rotman, 4th Edition, Graduate texts
in Mathematics, Springer-Verlag 1994.
- An Introduction to the Theory of Groups, J J Rotman, 3rd Edition, Wm C Brown Publishers,
1984.
- Representations and Characters of Groups, G James and M Liebeck, 2nd
Edition, Camb. Univ. Press, 2001
- Character Theory of Finite Groups, I M Isaacs, Dover Publications, 1994.
- A Course in the Theory of Groups, DJS Robinson,. Springer-Verlag, 1982.
- A Course on Group Theory, J S Rose, Dover Publications, INC, 1978.
- Introduction to the Theory of Finite Groups, W Ledermann, Oliver & Boyd, 1973.
- Group Theory, WR Scott, Prentice-Hall, 1964.
- The Theory of Groups, M Hall, Macmillan, 1959.

## Links:

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do with a Mathematics Major? MathWorld
Applications

Last updated:
02/20/08