Academic Year 2023-2024

HIGHER ALGEBRA 2

Teachers

Mario Mainardis
Unit Credits
6
Teaching Period
First Period
Course Type
Supplementary
Prerequisites. Undergraduate courses of di Arithmetics, Algebra1 (basic algebra).

Galois Theory ,

Geometry 1 (Linear Algebra).

Teaching Methods. Lectures with blackboard and chalk
Verification of Learning. Oral exam by appointment.
More Information. Upon request by the participants, the lectures may be held 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
Contents
The object of the course is the study of the finite simple groups. We’ll begin with recalling some basic results of the structure of a finite simple group, in particular the Theorem of Bender-Fitting. We shall then start with the structure of the alternating alternating groups and move from them to the major example, i.e. the projective special linear groups. We shall exhibit their decomposition as groups with BN-pairs, their simplicity and their automorphisms. Further we shall show how these results can be extended to all classical groups.

Time permitting we shall give some hints about the exceptional groups of Lie type and about some sporadic groups whose construction is relatively simple (Mathieu groups and Conway groups).

Texts
Robert A. Wilson.

The Finite Simple Groups, Springer Graduate Texts in Mathematics 2009

Lecture notes by the teacher