# Part IA - Groups

## Lectured by J. Goedecke, Michaelmas 2014

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

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# Contents

- V Full version
- 0 Introduction
- 1 Groups and homomorphisms
- 2 Symmetric group I
- 3 Lagrange's Theorem
- 4 Quotient groups
- 5 Group actions
- 6 Symmetric groups II
- 7 Quaternions
- 8 Matrix groups
- 8.1 General and special linear groups
- 8.2 Actions of GLn(C)
- 8.3 Orthogonal groups
- 8.4 Rotations and reflections in R2 and R3
- 8.5 Unitary groups
- 9 More on regular polyhedra
- 10 Mobius group
- 10.1 Mobius maps
- 10.2 Fixed points of Mobius maps
- 10.3 Permutation properties of Mobius maps
- 10.4 Cross-ratios
- 11 Projective line (non-examinable)