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**Modular Representation Theory of Finite Groups**## 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.

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**