Constructive recognition of classical groups in odd characteristic

C.R. Leedham-Green, E.A. O'Brien
2009 Journal of Algebra  
Let G = X GL(d, F ) be a classical group in its natural representation defined over a finite field F of odd characteristic. We present Las Vegas algorithms to construct standard generators for G which permit us to write an element of G as a straight-line program in X. The algorithms run in polynomial-time, subject to the existence of a discrete logarithm oracle for F .
doi:10.1016/j.jalgebra.2009.04.028 fatcat:2sbas3gmufbbldoyiwhqn6ygpe