Group Actions and Galois Theory

Table of Contents

  • Topics covered
  • Notes
  • TODO

    • Pre-Requisites

    Make sure to know all of the material from Abstract Algebra course from Year 2.

    Topics covered

    Group Actions

    1. Group Actions
    2. Orbits and Stabilizers
    3. Counting Orbits and Burnside Theorem
    4. Sylow Theorems
    5. Conjugacy
    6. Counting Orbits using Conjugacy Classes
    7. Subgroup Lattices

    Galois Theory

    1. Recap of Rings and Polynomial Rings (Irreducibility of Polynomials)
    2. Fields and Field Extensions
    3. Quotients of Rings
    4. Field Construction
    5. Constructibility I
    6. Vector Spaces and Degrees
    7. Constructibility II
    8. Splitting Fields
    9. Very Brief Groups Recap
    10. Galois Groups
    11. Not Solving Equations (i.e. Galois Theorem)

    Notes

    Galois Theory Notes

    TODO

    • Add a section on solubility
    • Maybe add a chapter on simple groups
    • Maybe add a section on homomorphisms on groups recap section although it is already covered in Year 2 notes

    Author: Akash Gopinath

    Created: 2024-12-31 Tue 23:14