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Normalisers of maximal tori and a conjecture of Vdovin
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Burness, Timothy C. and Thomas, Adam R. (2023) Normalisers of maximal tori and a conjecture of Vdovin. Journal of Algebra, 619 . pp. 459-504. doi:10.1016/j.jalgebra.2022.12.013 ISSN 0021-8693.
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Official URL: https://doi.org/10.1016/j.jalgebra.2022.12.013
Abstract
Let G = Op(G¯F ) be a finite simple group of Lie type defined over a field of characteristic p, where F is a Steinberg endomorphism of the ambient simple algebraic group G¯. Let T¯ be an F-stable maximal torus of G¯ and set N = NG(T¯). A conjecture due to Vdovin asserts that if G L3(2) then N ∩ Nx is a p-group for some x ∈ G. In this paper, we use a combination of probabilistic and computational methods to calculate the base size for the natural action of G on G/N, which allows us to prove a stronger, and suitably modified, version of Vdovin’s conjecture.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Journal of Algebra | ||||||||
Publisher: | Academic Press Inc Elsevier Science | ||||||||
ISSN: | 0021-8693 | ||||||||
Official Date: | 1 April 2023 | ||||||||
Dates: |
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Volume: | 619 | ||||||||
Page Range: | pp. 459-504 | ||||||||
DOI: | 10.1016/j.jalgebra.2022.12.013 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 15 December 2022 | ||||||||
Date of first compliant Open Access: | 9 January 2023 | ||||||||
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