Overview
The Classification of Finite Simple Groups was one of the biggest
achievements in 20th century group theory. By Jordan Hölder theorem, every finite group has a composition series
consisting of finite simple groups. So, finite simple groups can be seen as building blocks for all finite groups. According to the
classification theorem, a finite non-abelian simple group is either an alternating group, or a simple group of Lie type or one of the 26 sporadic groups
which are not belong to any infinite family. In this seminar, the theory of simple groups of Lie type as groups automorphisms of simple Lie algebras
will be discussed from the basics. The classical simple groups will be introduced and then root systems and Weyl groups, Chevalley groups and their structure
will be investigated. After dealing with automorphisms of Chevalley groups, at the end of the seminar, we will introduce some geometric structures associated with
simple groups of Lie type.
Seminar plan: A detailed plan of the talks will be available after the first meeting.
1st meeting : The Classical Simple Groups will be introduced (K. Ersoy)