This module will take place in the second semester, and will be about "Groups in Action". It will start with the basic ideas about a group acting on a set (orbits, stabilisers, etc), and we will see how these ideas can be used to solve various counting problems. We will then look at ways groups can act on themselves, and use these to prove Sylow's Theorems about subgroups of prime power order in a group. The final section of the course will be about representation theory, where we let the group act as linear transformations on a vector space (so that we have a homomorphism from the group to a suitable group of matrices).
Last updated: 27th May 2004