An algorithm for Lang's Theorem

JOURNAL OF ALGEBRA

卷:322

Article

Cohen, Arjeh M.¹  Murray, Scott H.² 

[1] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

[2] Univ Sydney, Dept Math & Stat F07, Sydney, NSW 2006, Australia

关键词: Lie algebra;    Linear algebraic group;    Chevalley basis;    Weyl group;    Derangements;    Las Vegas type algorithm;    Maximal total subalgebra;   

DOI  :  10.1016/j.jalgebra.2009.04.013

来源: Elsevier

【 摘 要 】

We give an efficient Las Vegas type algorithm for Lang's Theorem in split connected reductive groups defined over finite fields of characteristic greater than 3. This algorithm can be used to construct many important structures in finite groups of Lie type. We use an algorithm for computing a Chevalley basis for a split reductive Lie algebra, which is of independent interest. For our time analysis we derive that the proportion of reflection derangements in a Weyl group is less than 2/3. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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