The Kate Edger 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?
cl-finite-subgroups
cl-rubiks-cube

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.