Finite Simple Groups

Finite simple groups

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

5th March: New sample exam question (see below).
11th November: Slides of lectures 4 and 5 available from the links below. Also problem sheets 4 and 5.
21st October: Slides of lectures 2 and 3 available from the links below. Also problem sheets 2 and 3.
7th October: Problem sheet 1 available from the link below.
7th October: Slides of lecture 1 available from the link below.
Last year's page is available for backup, and until this year's page is ready.
16th September: Web-page in preparation.

Time: Mondays, 1.00-3.00 pm, 6th October - 10th November 2008, excluding 3rd November
Lecturer: Professor Robert A. Wilson, QMUL.

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.
- 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