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
18.
Free Groups and Presentations
18.1.
Free Groups
18.1.1.
Definition of Free Group
18.1.2.
Universal Property
18.1.3.
Reduced Words
18.1.4.
Rank of Free Groups
18.2.
Generators and Relations
18.2.1.
Group Presentations
18.2.2.
Defining Relations
18.2.3.
Word Problem
18.3.
Examples of Presentations
18.3.1.
Cyclic Groups
18.3.2.
Dihedral Groups
18.3.3.
Free Abelian Groups
18.4.
Von Dyck's Theorem
18.4.1.
Statement and Applications
18.4.2.
Quotients of Free Groups
18.5.
Tietze Transformations
18.5.1.
Elementary Operations
18.5.2.
Equivalence of Presentations
Previous
17. Composition Series and Jordan-Hölder Theorem
Go to top
Next
19. Semidirect Products