Intro to Abstract Algebra

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

Reflection

Aliases: reflection

Appears in:

  • Introduction to Groups: Dihedral Groups

Related ideas:

  • Dihedral Group
  • Isometry
  • Symmetry

Graph View

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