Groups and representations
Code
11588
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
António José Mesquita da Cunha Machado Malheiro
Weekly hours
4
Teaching language
Português
Subject matter
I. Group Theory
1. Basic notions.
2. Permutation groups.
3. Sylow Theorems.
4. Automorphism groups (including Jordan-Holder Theorem).
5. Soluble and Nilpotent groups.
[6. Finite abelian groups (optional)]
II. Representation Theory
1. Representations, modules and group algebras.
2. Mashke''''''''s Theorem and Schur''''''''s Lemma.
3. Character theory.
4. Applications (Burnside Theorems).
Bibliography
- John F. Humphreys, A course in group theory
- Ian D. Macdonald, The theory of groups
- John S. Rose, A course on group theory
- Joseph J. Rotman, An introduction to the theory of groups
- William Fulton and Joe Harris, Representation Theory (A first course)
- Gordon James and Martin Liebeck, Representations and Characters of Groups