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Abstract Algebra Topics


1. The Set of Integers


2. Types of Functions and Operations


3. Introduction to Groups

3.1. Introduction to Groups and Subgroups
3.2. Abelian Groups
3.3. Symmetric Groups, Permutation Groups, and Dihedral Groups
3.4. Cycles, Transpositions, and Alternating Groups
3.5. Cyclic Groups

4. Group Isomorphisms, Homomorphisms, and Automorphisms


5. External and Internal Direct Products, Cosets, Lagrange's Theorem, and Normal Subgroups


6. Introduction to Rings

6.1. Introduction to Rings and Subrings
6.2. Ideals, Quotient Rings, and Ring Homomorphisms/Isomorphisms/Automorphisms
6.3. Commutative Rings, Division Rings, and Integral Domains
6.4. Special Types of Integral Domains: PIDs, EDs, and UFDs

7. Introduction to Fields


8. Subnormal Series in a Group


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