Involution centralisers in finite unitary groups of odd characteristic

Stephen Glasby; Cheryl Praeger; Colva M. Roney-Dougal

doi:10.1016/j.jalgebra.2019.09.009

Involution centralisers in finite unitary groups of odd characteristic

Stephen Glasby, Cheryl Praeger, Colva M. Roney-Dougal

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	245-299
Journal	Journal of Algebra
Volume	545
Early online date	26 Sept 2019
DOIs	https://doi.org/10.1016/j.jalgebra.2019.09.009
Publication status	Published - 1 Mar 2020

Keywords

Involution centralisers
Recognition algorithms
Classical groups
Unitary groups
Regular semisimple elements
Group generation

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10.1016/j.jalgebra.2019.09.009

FINALuni_semisimple
Copyright © 2019 Elsevier Inc. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jalgebra.2019.09.009
Accepted author manuscript, 600 KBLicence: CC BY-NC-ND

Colva Roney-Dougal, OBE
- Colva.Roney-Dougalst-andrews.acuk
Person: Academic

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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.",

keywords = "Involution centralisers, Recognition algorithms, Classical groups, Unitary groups, Regular semisimple elements, Group generation",

author = "Stephen Glasby and Cheryl Praeger and Roney-Dougal, {Colva M.}",

note = "Funding: Australian Research Council Discovery Project grants DP160102323 and DP190100450.",

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AU - Praeger, Cheryl

AU - Roney-Dougal, Colva M.

N1 - Funding: Australian Research Council Discovery Project grants DP160102323 and DP190100450.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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.

AB - 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.

KW - Involution centralisers

KW - Recognition algorithms

KW - Classical groups

KW - Unitary groups

KW - Regular semisimple elements

KW - Group generation

U2 - 10.1016/j.jalgebra.2019.09.009

DO - 10.1016/j.jalgebra.2019.09.009

M3 - Article

SN - 0021-8693

VL - 545

SP - 245

EP - 299

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Involution centralisers in finite unitary groups of odd characteristic

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Keywords

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Colva Roney-Dougal, OBE

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