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. Group Representations

3.17.1. Group Representations

3.17.2. Maschke's Theorem

3.17.4. The Character of a Group Representation

3.17.5. The Left Regular Representation

3.18. Index of Common Groups

4. Rings

5. Fields

6. Subnormal Series in a Group

Submit an Error: Do you think that you see an error in any of the pages? Click the link and let us know so that we can fix it as soon as possible! All help is greatly appreciated with there being so many possible errors that can be overlooked.
  • 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.
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License