Intro to Abstract Algebra
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1. Introduction to Groups
Definitions and first examples
Basic algebra in a group
A first gallery of examples
Subgroups: first pass
Symmetric Groups
Dihedral Groups
Homomorphisms and isomorphisms: first pass
Group actions: first pass
2. Subgroups
Definitions and Examples
Generators and Relations
Cyclic Groups in Detail
3. Quotient Groups
Cosets and Lagrange’s Theorem
Normal subgroups
Quotient groups
Isomorphism Theorems
Composition Series and the Hölder Program
The classification of finitely generated abelian groups
4. Group Actions
Orbits and Stabilizers
The Class Equation
Other Group Actions with Applications
The action on left cosets
The action on subgroups by conjugation
5. Representation Theory
Definitions and Examples
Subrepresentations and irreducibility
Schur’s Lemma and Maschke’s Theorem
Characters
Characters and class functions
Computing Character Tables
Generator
Aliases:
generator
Appears in:
Subgroups: Cyclic Groups in Detail
Graph View