Involution centralisers in finite unitary groups of odd characteristic

2018/12/04 by S. P. Glasby, Cheryl E. Praeger, Glasby, S. P. +3
Computer Science · Mathematics · #20P05 #22E20 #60B20 #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1812.01362

openalex publication_date 2018/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Centralisers of Involutions in Black Box Groups
• Computations in Classical Groups
• Involutions in triangular groups
• Variants of some of the Brauer-Fowler Theorems
• A Note on Centralizers of Involutions in Coxeter Groups