Finite Simple Groups 2009

Finite simple groups 2009

A course of five 2-hour lectures given at the London postgraduate taught course centre, De Morgan House, Russell Square.

01/10/09: Last year's page is available for backup, and until this year's page is ready.

Preliminary reading
- I shall be assuming a basic knowledge of group theory, such is commonly taught in a UK undergraduate maths course. This material can be found in a condensed form in my notes, or in more extensive form in any decent book on group theory.
Lecture slides: the highlights
- Lecture 1.
- Lecture 2.
- Lecture 3. For display. For printing.
- Lecture 4.
- Lecture 5.
Lecture notes: the details
- First lecture. Alternating groups.
- Second lecture. The general linear groups; simplicity of PSL_n(q) via Iwasawa's Lemma.
- Third lecture. Forms and classical groups.
- Fourth lecture. Quaternions, octonions, and groups of type G₂
- Fifth lecture. Sporadic groups: M₂₄
Problem sheets
- Exercises 1. You probably won't want to do all these exercises: some good ones for testing your understanding are 5, 11, 12. If these are too hard, just start at the beginning and see how far you get.
  Selected hints and solutions.
- Exercises 2.
- Exercises 3.
- Exercises 4.
- Exercises 5.
Sample exam question