745 - Group Theory

This course will study finite groups, beginning with a review of
Sylow theory and ending with a purely group-theoretic proof of
Burnside's theorem that a group whose order involves just two primes
must be solvable. Some of the topics along the way are: split
extensions and semidirect products, the Schur-Zassenhaus theorem,
nilpotent groups and commutators, coprime action, transfer theory
and normal p-complements, Thompson's normal p-complement theorem.

There will be many problems available to work on, and course grades will
be based on solutions to ten of these problems handed in to be evaluated.