**Group Theory**

**SS 2017**

**Dietrich Burde**

**Lectures:** Monday 14:00 - 15:30 in SR09 and
Thursday 14:00 - 14:45 in SR09

**Exercises:** Thursday 15:00-15:45 in SR09

This page contains informations and pdf-files for this lecture and its exercise class.

Group theory is a broad subject which arises in many areas of mathematics and physics, and has
several different roots. One foundational root of group theory was the quest of solutions of polynomial
equations of degree higher than 4. Lagrange introduced permutation groups for the theory of equations,
and Galois the groups named after him for the solvability of the equation with radicals.
A second root was the study of symmetry groups in geometry.
The systematic use of groups in geometry was initiated by Klein's 1872 Erlangen program.
Finally, a third root of group theory was number theory. Certain abelian group structures had been
implicitly used in number-theoretical work by Gauss, and more explicitly by Kronecker.

Modern group theory nowadays is not just a part of abstract algebra. It has several branches, such as combinatorial
group theory, geometric group theory, the theory of finite groups, the theory of discrete groups, transformation groups,
Lie groups and algebraic groups, and many more. These lecture notes cover the topics stated in the curriculum for
master mathematics at the university of Vienna.

Here is a syllabus and a bibliography available.

##
pdf-files:

No. |
Topic |
Date |
pdf-file |

1 |
Exercises |
2017 |
groups.pdf |

**Topics for the exam**:

- Basic notions and examples, Sylow theorems and semidirect products.
- Subnormal series, solvable and nilpotent groups
- Free groups and presentations by generators and relations
- Group extensions and factor systems
- Cohomology of groups

Dietrich Burde
Last modified: Mon Feb 27 17:24:35 CET 2017