Group Theory
Normal Subgroup Criterion
Conjugation Characterization
Examples of Normal Subgroups
Conjugation Test
Index 2 Subgroups
Kernel Test
Center and Derived Subgroup
Conjugate Elements
Conjugate Subgroups
Conjugacy Classes
Definition of Coset Multiplication
Well-definedness of the Operation
Verification of Group Axioms
ℤ/nℤ as a Quotient Group
Dₙ/⟨r⟩
Sₙ/Aₙ ≅ ℤ/2ℤ
Order of Quotient Groups
Abelian Quotients
Definition of a Simple Group
Examples of Simple Groups
Simplicity of Aₙ for n ≥ 5
Classification Overview
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8. Cosets and Lagrange's Theorem
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10. Group Homomorphisms