Solvable groups

Lecturer

Schedule

The intensive course Solvable groups will be held at the University of Tampere in the Department of Mathematics, Statistics and Philosophy. The course starts on Tuesday 25.5. and ends on Thursday 3.6.2004. The lectures will be held at Pinni A2093 (Tue-Fri, Mon-Thu) at 10-12.

Contents

1. Introduction and motivation from Galois theory
2. Preliminaries from finite group theory (conjugacy classes, normalizers, proof of Sylow theorems by induction)
3. Commutators and solvable finite groups
4. Solvability criteria for finite groups (by using subgroups, factors and order)
5. Generalizing the Sylow theorems in the case of finite solvable groups (existence of Hall subgroups)
6. Characterization of the class of finite abelian/nilpotent/solvable groups by 2-variable identities.

Context

This intensive course is one in the series of algebra courses arranged in connection to the Finite Model Theory project:

• 2002 Non-associative binary systems (Ales Drapal)
• 2003 Permutation groups (Rick Thomas)
• 2004 Soluble groups (Markku Niemenmaa)

Course material

Lecture notes for the course in dvi-form and in ps-form.

Department of Mathematics

Finite model theory in Finland

Teaching of mathematical logic