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**Algorithms for Group Theory**## Department of Mathematics

# Algorithms for Group Theory

This research focuses on on the development, analysis, and application of high-quality algorithms to group theory and other areas of computational algebra.

We study such questions as:

- How fast can we compute M
^{n}where M is a 100 x 100 matrix and n = 10^{20}? - How can we compute a Jordan canonical form for a matrix?
- How do we explore the group of symmetries of the Rubik cube, and prove that it has 43252003274489856000 elements?
- How do we verify that every element in a group of order 7
^{20416}has order dividing 7? - How do we construct a random element in the Monster M, containing 808017424794512875886459904961710757005754368000000000 elements?
- What does this diagram mean and how can we verify it?

- 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**