Math 8851. Course outline

The course will consist of four main parts:

A.  Free groups and presentations of groups by generators and relations (9 lectures)
B.  Word growth in groups (4 lectures)
C.  Structure theory of linear groups (5 lectures)
D.  Commutator calculus and the Burnside problem(s) (6 lectures)

Detailed schedule (very preliminary version)


There is no official text for the course. Some (but not all) of the material we will discuss is covered by the following books:


The course should be accessible to students who have completed first year graduate courses. The main prerequisite is a good knowledge of  basic group theory at the level of Math 7751 (e.g. the first six chapters of Dummit and Foote) and linear algebra. However, occasionally we will use results from other areas, including topology (mainly covering spaces) and ring theory.

Homework and Problem Session

End of the semester Presentations

Each student must give a 30 minute presentation on the topic of her/his choice during the last 3-4 classes. A list of suggested topics will be provided. You should feel free to choose a different topic (not from the list), but you need to get my approval. In any case,  you should inform me about your proposed topic no later than the end of October.