In the course (6 credits) we present basic ideas of representation theory for finite groups.
1. Definitions and examples. Irreducible, reducible and completely reducible representations of finite groups. 2. Representations and modules. Simple and semisimple modules: characterizations. 3. Applications to the group algebra. Maschke's Theorem. 4. Characters of finite groups Basic definitions and properties, irreducible characters, orthogonality relations, linear characters. 5. Character tables. Examples. 6. Applications of Character Theory. Solubility criteria, Burnside's Theorem, existence of normal subgroups and how to determine them. 7. Product of representations. 8. Induced representations and characters. Frobenius' Theorem. 9. Representations of symmetric groups. Partitions and Young tableaux, degrees of the irreducible representations of .