This intensive course will be held 4 June  13 June 2003 (WedSat, MonFri) at the University of Helsinki in the Department of Mathematics.
Time  Lecture room
 
Wednesday 4.6.  1214  SIII

Thursday 5.6.  1214  SIII

Friday 6.6.  1013  SIII

Saturday 7.6.  1012  SIII

Monday 9.6.  1013  SIV

Tuesday 10.6.  1012  SIV

Wednesday 11.6.  1012  SIV

Thursday 12.6.  1012  SIV

Friday 13.6.  1012  SIV

The purpose of this course is to give an introduction to some topics in the theory of permutation groups.
We do not presume much in the way of assumed knowledge: essentially just some elementary group theory (such as the notion of a normal subgroup). We will cover the prerequisites at the start of the course. There will also be a survey of the relevant properties of the alternating and symmetric groups.
After this introduction, we will then cover the basics of permutation groups, such as the notions of permutation representations, orbits and stabilizers, and we will show how these ideas allow us to prove results in group theory (such as Sylow's theorems). We will also cover Burnside's lemma.
Following on, we look at the notions of multiple transitivity and primitivity, and demonstrate properties of groups having permutation representations of this kind (such as properties of normal subgroups). We will also give an indication of more advanced topics, such as Jordan groups and the O'NanScott theorem.
Throughout the course, we will be giving examples showing how these notions relate to other areas of mathematics (such as graph theory).
This intensive course is one in the series of algebra courses arranged in connection to the Finite Model Theory project:
Department of Mathematics  Finite model theory in Finland  Teaching of mathematical logic 