Academic Year 2021-2022



Mario Mainardis
Unit Credits
Teaching Period
First Period
Course Type
Prerequisites. Algebra 1, Geometria 1, Teoria di Galois
Teaching Methods. Front lectures with chalk and blackboard.

From time to time the students will be given problems to be solved.

Verification of Learning. Oral proof on a date to be agreed with the teacher.
More Information. On request the lectures can be kept in English.
Understand the relations between a finite group and its table of irreducible characters. In particular be able to get information on a group from its character table
1. Algebras, modules, and representations.

2. Group representations and characters.

3. Arithmetical and geometrical properties of characters. Burnside’s (p^a)(q^b) Theorem and the character table.

4. induced characters.

5. Normal subgroups.

6. Trivial intersection sets and exceptional characters, existence of the Frobenius kernel.

7. Complements

1) I. M. Isaacs,

Character Theory of Finite Groups, New York 1976.

2) N. Jacobson, Basic Algebra 2, New York, 1989.

G. James, M. Liebeck, Representations and Characters of Groups, Cambridge mathematical Textbooks 1995.