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dc.contributor.authorBray, John
dc.contributor.authorCai, Qi
dc.contributor.authorCameron, Peter Jephson
dc.contributor.authorSpiga, Pablo
dc.contributor.authorZhang, Hua
dc.date.accessioned2020-03-07T00:32:23Z
dc.date.available2020-03-07T00:32:23Z
dc.date.issued2020-03
dc.identifier.citationBray , J , Cai , Q , Cameron , P J , Spiga , P & Zhang , H 2020 , ' The Hall–Paige conjecture, and synchronization for affine and diagonal groups ' , Journal of Algebra , vol. 545 , pp. 27-42 . https://doi.org/10.1016/j.jalgebra.2019.02.025en
dc.identifier.issn0021-8693
dc.identifier.otherPURE: 257874442
dc.identifier.otherPURE UUID: 71831364-14c8-425a-87cc-def11c7c07e8
dc.identifier.otherORCID: /0000-0003-3130-9505/work/58055599
dc.identifier.otherScopus: 85062707973
dc.identifier.otherWOS: 000508288800003
dc.identifier.urihttp://hdl.handle.net/10023/19613
dc.description.abstractThe Hall-Paige conjecture asserts that a finite group has a complete mapping if and only if its Sylow subgroups are not cyclic. The conjecture is now proved, and one aim of this paper is to document the final step in the proof (for the sporadic simple group J4). We apply this result to prove that primitive permutation groups of simple diagonal type with three or more simple factors in the socle are non-synchronizing. We also give the simpler proof that, for groups of affine type, or simple diagonal type with two socle factors, synchronization and separation are equivalent. Synchronization and separation are conditions on permutation groups which are stronger than primitivity but weaker than 2-homogeneity, the second of these being stronger than the first. Empirically it has been found that groups which are synchronizing but not separating are rather rare. It follows from our results that such groups must be primitive of almost simple type.
dc.language.isoeng
dc.relation.ispartofJournal of Algebraen
dc.rights© 2019, Elsevier, Inc. This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jalgebra.2019.02.025en
dc.subjectAutomataen
dc.subjectComplete mappingsen
dc.subjectGraphsen
dc.subjectHall-Paige conjectureen
dc.subjectOrbitalsen
dc.subjectPrimitive groupsen
dc.subjectSeparating groupsen
dc.subjectSynchronizing groupsen
dc.subjectTransformation groupsen
dc.subjectQA Mathematicsen
dc.subjectMathematics(all)en
dc.subjectT-NDASen
dc.subjectBDCen
dc.subject.lccQAen
dc.titleThe Hall–Paige conjecture, and synchronization for affine and diagonal groupsen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.1016/j.jalgebra.2019.02.025
dc.description.statusPeer revieweden
dc.date.embargoedUntil2020-03-08


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