SUBJECT
Title
Groups and representations
Type of instruction
lecture + practical
Level
master
Faculty
Part of degree program
Credits
2+3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Group actions, permutation groups, automorphism groups. Semidirect products. Sylow’s Theorems.
Finite p-groups. Nilpotent groups. Solvable groups, Phillip Hall’s Theorems.
Free groups, presentations, group varieties. The Nielsen-Schreier Theorem.
Abelian groups. The Fundamental Theorem of finitely generated Abelian groups. Torsionfree groups.
Linear groups and linear representations. Semisimple modules and algebras. Irreducible representations. Characters, orthogonality relations. Induced representations, Frobenius reciprocity, Clifford’s Theorems.
Readings
- D.J.S. Robinson: A course in the theory of groups, Springer, 1993
- I.M. Isaacs: Character theory of finite groups, Academic Press, 1976