Covering numbers for simple algebraic groups
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Published version
Author(s)
Liebeck, Martin
Simion, Iulian
Type
Journal Article
Abstract
Let G be a simple algebraic group over an algebraically closed field, and let C be a noncentral conjugacy class of G. The covering number cn(G, C) is defined to be the minimal k such that G = Ck , where Ck = {c1c2 · · · ck : ci ∈ C}. We prove that cn(G, C) ≤ c dim G dim C , where c is an explicit constant (at most 120). Some consequences on the width and generation of simple algebraic groups are given.
Date Issued
2023-07-01
Date Acceptance
2022-11-06
Citation
Vietnam Journal of Mathematics, 2023, 51 (3), pp.605-616
ISSN
0866-7179
Publisher
Springer Verlag
Start Page
605
End Page
616
Journal / Book Title
Vietnam Journal of Mathematics
Volume
51
Issue
3
Copyright Statement
© The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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Publication Status
Published
Date Publish Online
2023-03-01