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dc.contributor.authorMoscatiello, Mariapia
dc.contributor.authorRoney-Dougal, Colva M.
dc.identifier.citationMoscatiello , M & Roney-Dougal , C M 2021 , ' Base sizes of primitive permutation groups ' , Monatshefte für Mathematik , vol. First Online .
dc.identifier.otherPURE: 274764761
dc.identifier.otherPURE UUID: 9eef3bc0-c302-43c2-aa58-93da4f1bbb18
dc.identifier.otherORCID: /0000-0002-0532-3349/work/98487623
dc.identifier.otherScopus: 85111934239
dc.identifier.otherWOS: 000681580500001
dc.descriptionThis work was supported by: EPSRC Grant Numbers EP/R014604/1 and EP/M022641/1.en
dc.description.abstractLet G be a permutation group, acting on a set Ω of size n. A subset B of Ω is a base for G if the pointwise stabilizer G(B) is trivial. Let b(G) be the minimal size of a base for G. A subgroup G of Sym(n) is large base if there exist integers m and r ≥ 1 such that Alt (m)r ... G ≤ Sym (m) \wr Sym (r), where the action of Sym (m) is on k-element subsets of {1,...,m} and the wreath product acts with product action. In this paper we prove that if G is primitive and not large base, then either G is the Mathieu group M24 in its natural action on 24 points, or b(G) ≤ ⌈log n⌉ + 1. Furthermore, we show that there are infinitely many primitive groups G that are not large base for which b(G) > log n + 1, so our bound is optimal.
dc.relation.ispartofMonatshefte für Mathematiken
dc.rightsCopyright © The Author(s) 2021. Open Access. 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
dc.subjectPrimitive groupsen
dc.subjectBase sizeen
dc.subjectClassical groupsen
dc.subjectSimple groupsen
dc.subjectQA Mathematicsen
dc.titleBase sizes of primitive permutation groupsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews.St Andrews GAP Centreen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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