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Author(s): J. Goedecke, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part IA Lecture Notes
Publisher: University of Cambridge
Year: 2014

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; group theory; abstract algebra; modern algebra; rings; fields; ring; field; modules; module

Introduction
Groups and homomorphisms
Groups
Homomorphisms
Cyclic groups
Dihedral groups
Direct products of groups
Symmetric group I
Symmetric groups
Sign of permutations
Lagrange's Theorem
Small groups
Left and right cosets
Quotient groups
Normal subgroups
Quotient groups
The Isomorphism Theorem
Group actions
Group acting on sets
Orbits and Stabilizers
Important actions
Applications
Symmetric groups II
Conjugacy classes in Sn
Conjugacy classes in An
Quaternions
Matrix groups
General and special linear groups
Actions of GLn(C)
Orthogonal groups
Rotations and reflections in R2 and R3
Unitary groups
More on regular polyhedra
Symmetries of the cube
Symmetries of the tetrahedron
Mobius group
Mobius maps
Fixed points of Mobius maps
Permutation properties of Mobius maps
Cross-ratios
Projective line (non-examinable)