HIGHER ALGEBRA 2

Academic Year 2021-2022

Teachers

Mario Mainardis

Unit Credits

Teaching Period

First Period

Course Type

Supplementary

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.

Objectives

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

Texts

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.

Academic Year 2021-2022

HIGHER ALGEBRA 2

Mario Mainardis

Unit Credits

Teaching Period

Course Type

Objectives

Contents

Texts

CONTATTI

INTERNATIONAL COORDINATES

LINK UTILI