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 Mn where M is a 100 x 100 matrix and n = 1020?
  • 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 720416 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?

As part of this work, we make extensive use of computational algebra packages, and our software is distributed with these.

Researchers at The University of Auckland:


Research is supported by the New Zealand Marsden Fund.