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The intersection graph of a finite simple group has diameter at most 5
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dc.contributor.author | Freedman, Saul D. | |
dc.date.accessioned | 2021-02-18T10:30:06Z | |
dc.date.available | 2021-02-18T10:30:06Z | |
dc.date.issued | 2021-07 | |
dc.identifier | 272521562 | |
dc.identifier | dc4b8a79-a151-47c9-bb77-cbfa51e6a99c | |
dc.identifier | 85100905932 | |
dc.identifier | 000617829500001 | |
dc.identifier.citation | Freedman , 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/s00013-021-01583-3 | en |
dc.identifier.issn | 0003-889X | |
dc.identifier.uri | https://hdl.handle.net/10023/21446 | |
dc.description | The 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.abstract | Let 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.extent | 7 | |
dc.format.extent | 266804 | |
dc.language.iso | eng | |
dc.relation.ispartof | Archiv der Mathematik | en |
dc.subject | Intersection graph | en |
dc.subject | Simple group | en |
dc.subject | Subgroups | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | NIS | en |
dc.subject.lcc | QA | en |
dc.title | The intersection graph of a finite simple group has diameter at most 5 | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1007/s00013-021-01583-3 | |
dc.description.status | Peer reviewed | en |
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