Involution centralisers in finite unitary groups of odd characteristic

JOURNAL OF ALGEBRA

卷:545

Article

Glasby, S. P.¹  Praeger, Cheryl E.¹  Roney-Dougal, Colva M.² 

[1] UWA, Dept Math & Stat, Perth, WA 6009, Australia

[2] Univ St Andrews, Math Inst, St Andrews KY16 9SS, Fife, Scotland

关键词: Involution centralisers;    Recognition algorithms;    Classical groups;    Unitary groups;    Regular semisimple elements;    Group generation;   

DOI  :  10.1016/j.jalgebra.2019.09.009

来源: Elsevier

【 摘 要 】

We analyse the complexity of constructing involution centralisers in unitary groups over fields of odd order. In particular, we prove logarithmic bounds on the number of random elements required to generate a subgroup of the centraliser of a strong involution that contains the last term of its derived series. We use this to strengthen previous bounds on the complexity of recognition algorithms for unitary groups in odd characteristic. Our approach generalises and extends two previous papers by the second author and collaborators on strong involutions and regular semisimple elements of linear groups. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free