Constructive recognition of classical groups in odd characteristic

摘要

Let G____5 GL(d. F) be a classical group in its natural represen_tation 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.