Groups and representations
António José Mesquita da Cunha Machado Malheiro
Weekly - 4
Total - 52
- 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)
- Benjamin Steinberg, Representation Theory of Finite Groups - An Introductory Approach-Springer Verlag New York (2012)
The main topics and results will be presented in lectures, and must be suplemented with the reading of the referenced book. Exercises are proposed to complement the study. Students are invited to present their work and their difficulties to the teacher during the attendance time and also by email.
The assessment is made by continuous evaluation.
The continuous evaluation consists of three individual examinations. The final grade is the average of the test scores rounded to the nearest unit. In the case of obtaining a score greater than 16, the student may choose between having a complimentary exam to the defense of the grade, or stay with a final grade of 16 points.
The final exam is written and lasts for 3 hours.
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).
Programs where the course is taught: