UsefulLinks
Mathematics
Group Theory
1. Introduction to Algebraic Structures
2. Definition of a Group
3. Fundamental Examples of Groups
4. Order of Elements and Groups
5. Subgroups
6. Cyclic Groups
7. Permutation Groups
8. Cosets and Lagrange's Theorem
9. Normal Subgroups and Quotient Groups
10. Group Homomorphisms
11. The Isomorphism Theorems
12. Group Actions
13. The Sylow Theorems
14. Direct Products and Sums
15. Structure of Finite Abelian Groups
16. Solvable and Nilpotent Groups
17. Composition Series and Jordan-Hölder Theorem
18. Free Groups and Presentations
19. Semidirect Products
20. Introduction to Representation Theory
21. Applications of Group Theory
19.
Semidirect Products
19.1.
Definition and Construction
19.1.1.
External Semidirect Product
19.1.2.
Internal Semidirect Product
19.1.3.
Action by Automorphisms
19.2.
Examples and Properties
19.2.1.
Dihedral Groups as Semidirect Products
19.2.2.
Affine Groups
19.2.3.
Holomorphs
19.3.
Classification Results
19.3.1.
Groups of Order pq
19.3.2.
Extensions of Groups
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18. Free Groups and Presentations
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20. Introduction to Representation Theory