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
In this 2-page handout we discuss an isomorphism between the real numbers under addition〈R, +〉, and the positive real numbers under multiplication〈R+, ·〉. This is a great example to deepen your understanding of isomorphisms.
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Cycles in Groups
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