Group Theory
Left Actions
Right Actions
Faithful Actions
Left Regular Action
Right Regular Action
Action by Conjugation
Action on Cosets
Action on Subgroups
Linear Actions
Definition and Properties
Orbit Decomposition
Transitive Actions
Isotropy Subgroups
Pointwise and Setwise Stabilizers
Statement and Proof
Applications and Examples
Counting Orbits
Definition and Examples
Fixed Point Sets
Free Actions
Cauchy-Frobenius Lemma
Applications to Counting
Pólya Enumeration
Conjugacy Classes
Class Equation
Applications to p-Groups
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11. The Isomorphism Theorems
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13. The Sylow Theorems