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dc.contributor.authorMoscatiello, Mariapia
dc.contributor.authorRoney-Dougal, Colva M.
dc.date.accessioned2021-08-11T10:30:06Z
dc.date.available2021-08-11T10:30:06Z
dc.date.issued2021-08-05
dc.identifier274764761
dc.identifier9eef3bc0-c302-43c2-aa58-93da4f1bbb18
dc.identifier85111934239
dc.identifier000681580500001
dc.identifier.citationMoscatiello , M & Roney-Dougal , C M 2021 , ' Base sizes of primitive permutation groups ' , Monatshefte für Mathematik , vol. First Online . https://doi.org/10.1007/s00605-021-01599-5en
dc.identifier.issn0026-9255
dc.identifier.otherORCID: /0000-0002-0532-3349/work/98487623
dc.identifier.urihttps://hdl.handle.net/10023/23758
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.format.extent33
dc.format.extent442728
dc.language.isoeng
dc.relation.ispartofMonatshefte für Mathematiken
dc.subjectPrimitive groupsen
dc.subjectBase sizeen
dc.subjectClassical groupsen
dc.subjectSimple groupsen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleBase sizes of primitive permutation groupsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
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.identifier.doi10.1007/s00605-021-01599-5
dc.description.statusPeer revieweden
dc.date.embargoedUntil2021-08-05
dc.identifier.grantnumberEP/M022641/1en


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