Involution centralisers in finite unitary groups of odd characteristic

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

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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.
Original languageEnglish
Pages (from-to)245-299
JournalJournal of Algebra
Volume545
Early online date26 Sept 2019
DOIs
Publication statusPublished - 1 Mar 2020

Keywords

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

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