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Abstract Algebra Topics


1. The Set of Integers


2. Types of Functions and Operations


3. Groups

3.1. Introduction to Groups and Subgroups

3.1.1. Groups, Subgroups, and Basic Properties of Groups

3.1.2. The Order of Elements in a Group

3.1.3. Examples of Groups:

3.8. Centers, Centralizers, Normalizers, and Normal Subgroups

3.8.1. The Center of a Group and Centralizers

3.8.2. Normalizers

3.8.3. Normal Subgroups of a Group

3.8.4. Simple Groups

3.9. Direct Products

3.9.1. The Product of Two Subgroups

3.9.2. Direct Products of Groups

3.9.3. The Internal Direct Product

3.9.4. The Fundamental Theorem of Finite Abelian Groups

3.15. The Sylow Theorems

3.15.1. Sylow p-Subgroups and The Sylow Theorems

3.16. Solvable Groups

3.16.1. Composition Series and the Jordan-Hölder Theorem

3.16.2. Commutators and the Derived Subgroup of a Group

3.16.3. Solvable Groups

3.16.4. Characteristic Subgroups of a Group

3.17. Index of Common Groups

4. Rings


5. Fields


6. Subnormal Series in a Group


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References
  • 1. Abstract Algebra (3rd Edition) by John A. Beachy and William D. Blair.
  • 2. Abstract Algebra (3rd Edition) by David S. Dummit and Richard M. Foote.
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