Constructive homomorphisms for classical groups

  • Authors:

  • Scott H. Murray;Colva M. Roney-Dougal

  • Affiliations:

  • Discipline of Mathematics and Statistics, Faculty of Information Sciences and Engineering, Building 11, University of Canberra, ACT, 2601, Australia;School of Mathematics and Statistics, University of St Andrews, Fife KY16 9SS, UK

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

Abstract

Let @W@?GL(V) be a quasisimple classical group in its natural representation over a finite vector space V, and let @D=N"G"L"("V")(@W). We construct the projection from @D to @D/@W and provide fast, polynomial-time algorithms for computing the image of an element. Given a discrete logarithm oracle, we also represent @D/@W as a group with at most 3 generators and 6 relations. We then compute canonical representatives for the cosets of @W. A key ingredient of our algorithms is a new, asymptotically fast method for constructing isometries between spaces with forms. Our results are useful for the matrix group recognition project, can be used to solve element conjugacy problems, and can improve algorithms to construct maximal subgroups.