Constructive recognition of classical groups in even characteristic

JOURNAL OF ALGEBRA

卷:391

Article

Dietrich, Heiko¹  Leedham-Green, C. R.²  Luebeck, Frank³  O'Brien, E. A.⁴ 

[1] Monash Univ, Sch Math Sci, Clayton, Vic 3800, Australia

[2] Univ London, Sch Math Sci, London E1 4NS, England

[3] Rhein Westfal TH Aachen, Lehrstuhl Math, D-52062 Aachen, Germany

[4] Univ Auckland, Dept Math, Auckland, New Zealand

关键词: Classical groups;    Constructive recognition;    Even characteristic;   

DOI  :  10.1016/j.jalgebra.2013.04.031

来源: Elsevier

【 摘 要 】

Let G = < X > <= GL(d, F) be a classical group in its natural representation defined over a finite field IF of even 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, and to construct an involution as a straight-line program in X. If vertical bar F vertical bar > 4, then the algorithms run in time polynomial in the size of the input, subject to the existence of a discrete logarithm oracle for F. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free