Constructive homomorphisms for classical groups

Let Ω ≤ GLd(q) be a quasisimple classical group in its natural representation and let ∆ = NGLd(q)(Ω). We construct the projection from ∆ to ∆/Ω and provide fast, polynomialtime algorithms for computing the image of an element. Given a discrete logarithm oracle, we also represent ∆/Ω as a group with at most 3 generators and 6 relations. We then compute canonical representatives for the cosets of Ω. We describe applications of these methods to the matrix group recognition project and conjugacy problems. A key ingredient of our algorithms is a new, asymptotically fast method for constructing isometries between spaces with bilinear or unitary forms.

• Type: Journal
• Year: 2011
• Where: JSC
• Authors: Scott H. Murray, Colva M. Roney-Dougal
• Keywords: Discrete Logarithm Oracle, JSC 2011, Matrix Group Recognition, Quasisimple Classical Group