### 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)

### References

There is no official text for the course. Some (but not all) of the
material
we will discuss is covered by the following books:
*A course in the theory of groups * by D. Robinson
*Combinatorial group theory * by W. Magnus, A. Karrass and
D. Solitar
*Combinatorial group theory * by R. C. Lyndon and
P.E. Schupp
*Topics in geometric group theory * by P. de la Harpe
- Infinite linear groups
by B. A. F. Wehrfritz

*p-automorphisms of finite p-groups * by E.I. Khukhro

### Prerequisities

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

- Homework will be assigned weekly

- Approximately every two weeks we will have a problem session
(date and time TBD) where homework problems will be discussed.

- Graduate students taking the class are expected to present
homework problems during the problem sessions on the regular basis

- Undergraduate students taking this class must submit all
homework assignments in writing by the given due dates

### 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.