University Maths Notes - Albstract Algebra and Group Theory

University Maths Notes: Abstract Algebra and Group Theory

Introduction to Group theory	Cyclic Groups
Conjugacy	Cosets
Field Axioms	Galois Theory and Solubility of Polynomial Equations by Radicals
Group Actions	Integral Domains
Kernels and Images of Homomorphisms	Morphisms
Permutation Groups	Quotient Groups
Ring Axioms	Subgroups
The Orbit Stabilizer Theorem	Cayley Tables
Sylow's First Theorem	Sylow's Second Theorem
Sylow's Third Theorem	The Internal Direct Product Theorem for Finite Groups
Cayley's Theorem	Simple Groups
The First Isomorphism Theory	Classifying Small Groups of Finite Order
The Conjugacy Class Equation