Projects and Assignments in Pure Mathematics
Combinatorial group theory
This is the study of groups described by a collection of generators
(so every member of the group can be written as a product of a sequence of these generators) and
relations holding among these generators.
Early material would cover free groups (for which there are no relations), and free products of groups.
Typical later material would concern free products with amalgamation and HNN extensions, and connections
might well be made to algebraic topology (eg if done as 4MM).
It is best
done either as 4MM, or in the second semester as 3083, after a student has done Groups and Symmetry (3071).
Books
R.C. Lyndon, P.E. Schupp, Combinatorial Group Theory, Springer, 1977.
W. Magnus, A. Karrass, D. Solitar, Combinatorial Group theory, Wiley, 1966.
Pure projects homepage