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The intersection graph of a finite simple group has diameter at most 5

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dc.contributor.authorFreedman, Saul D.
dc.date.accessioned2021-02-18T10:30:06Z
dc.date.available2021-02-18T10:30:06Z
dc.date.issued2021-07
dc.identifier.citationFreedman , S D 2021 , ' The intersection graph of a finite simple group has diameter at most 5 ' , Archiv der Mathematik , vol. 117 , no. 1 , pp. 1-7 . https://doi.org/10.1007/s00013-021-01583-3en
dc.identifier.issn0003-889X
dc.identifier.otherPURE: 272521562
dc.identifier.otherPURE UUID: dc4b8a79-a151-47c9-bb77-cbfa51e6a99c
dc.identifier.otherScopus: 85100905932
dc.identifier.otherWOS: 000617829500001
dc.identifier.urihttps://hdl.handle.net/10023/21446
dc.descriptionThe author was supported by a St Leonard’s International Doctoral Fees Scholarship and a School of Mathematics & Statistics PhD Funding Scholarship at the University of St Andrews.en
dc.description.abstractLet G be a non-abelian finite simple group. In addition, let ΔG be the intersection graph of G, whose vertices are the proper non-trivial subgroups of G, with distinct subgroups joined by an edge if and only if they intersect non-trivially. We prove that the diameter of ΔG has a tight upper bound of 5, thereby resolving a question posed by Shen (Czechoslov Math J 60(4):945–950, 2010). Furthermore, a diameter of 5 is achieved only by the baby monster group and certain unitary groups of odd prime dimension.
dc.format.extent7
dc.language.isoeng
dc.relation.ispartofArchiv der Mathematiken
dc.rightsCopyright © 2021 The Author(s). 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 http://creativecommons.org/licenses/by/4.0/.en
dc.subjectIntersection graphen
dc.subjectSimple groupen
dc.subjectSubgroupsen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectNISen
dc.subject.lccQAen
dc.titleThe intersection graph of a finite simple group has diameter at most 5en
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1007/s00013-021-01583-3
dc.description.statusPeer revieweden


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