Course curriculum

    1. Welcome to Group Theory

    2. Support Socratica

    1. Group Definition

    2. Example 1: The Integers

    3. Example 2: Vectors

    4. Example 3: Nonzero Real Numbers

    5. Subgroups - Definition & Examples

    6. Group Multiplication Tables (Cayley Tables)

    7. Cosets and Lagrange's Theorem

    1. Cyclic Groups

    2. Symmetries of a Triangle

    3. Dihedral Group

    4. Group Example - S1

    5. Symmetric Groups

    6. Cycle Notation for Permutations

    7. Matrix Groups

    1. Group Homomorphisms

    2. The Kernel of a Homomorphism

    3. Normal Subgroups and Factor Groups

    4. Isomorphisms - Example 1

    5. Automorphisms

    1. Direct Products of Groups

    1. Simple Groups

About this course

  • Free
  • 25 lessons
  • 2 hours of video content

Group Theory Topics

We focus on the main topics to help you see the forest for the trees

  • Learn the motivation and definition of the central concept in abstract algebra - the group

  • See many examples of groups including symmetric groups, dihedral groups, matrix groups, and more

  • Explore the concept of "homomorphism", a technique for comparing two groups to see how similar - or dissimilar - they are from each other

Évariste Galois

Learn about the young mathematician who was instrumental in developing the concept of a group and developing what has become known as Galois Theory.

Release Notes

Version 1.02

2024-02-09: Group example - nonzero real numbers
2024-01-23: Example of how vectors for an abelian group
2024-01-18: Added lesson on subgroups
2024-01-17: Examples added to "Introduction to Groups"
2024-01-16: Work on course introduction
2023-10-07: Initial release