Department of Mathematics


Modular Representation Theory of Finite Groups

A modular representation of a group is a homomorphism from the group to a matrix group over a field with positive characteristic p.

Representation theory is the study of the various representations of a group. The research focuses on the determination of a group from the knowledge of its p-local subgroups. Here a p-local subgroup is the normalizer of a p-subgroup such as the normalizer of a Sylow p-subgroup. This is also known as local representation theory.

We study such questions as:

  • What can we say about the group if we know the structure of a Sylow p-subgroup?
  • How many proper p-local subgroups determine the structure of a given finite group?
  • How can we construct such p-local subgroups?
  • How can we get the representations of the group from the representations of p-local subgroups?

Researchers at The University of Auckland

 

Research is supported by the New Zealand Marsden Fund.