Group Theory
Your Abstract Algebra Journey Begins Here
Welcome to Group Theory
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Group Definition
Example 1: The Integers
Example 2: Vectors
Example 3: Nonzero Real Numbers
Subgroups - Definition & Examples
Group Multiplication Tables (Cayley Tables)
Cosets and Lagrange's Theorem
Cyclic Groups
Symmetries of a Triangle
Dihedral Group
Group Example - S1
Symmetric Groups
Cycle Notation for Permutations
Matrix Groups
Group Homomorphisms
The Kernel of a Homomorphism
Normal Subgroups and Factor Groups
Isomorphisms - Example 1
Automorphisms
Direct Products of Groups
Simple Groups
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
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