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dc.contributor.authorKelsey, Veronica
dc.contributor.authorRoney-Dougal, Colva Mary
dc.identifier.citationKelsey , V & Roney-Dougal , C M 2022 , ' Maximal cocliques in the generating graphs of the alternating and symmetric groups ' , Combinatorial Theory , vol. 2 , no. 1 , 56879 .
dc.identifier.otherPURE: 277355413
dc.identifier.otherPURE UUID: 33d2a6b6-ea56-4204-9fb2-caeb4e9a544b
dc.identifier.otherORCID: /0000-0002-0532-3349/work/111210046
dc.identifier.otherORCID: /0000-0001-7642-7391/work/111210312
dc.descriptionFunding: This work was supported by EPSRC grant number EP/R014604/1. In addition, this work was partially supported by a grant from the Simons Foundation.en
dc.description.abstractThe generating graph Γ (G) of a finite group G has vertex set the non-identity elements of G, with two elements adjacent exactly when they generate G. A coclique in a graph is an empty induced subgraph, so a coclique in Γ (G) is a subset of G such that no pair of elements generate G. A coclique is maximal if it is contained in no larger coclique. It is easy to see that the non-identity elements of a maximal subgroup of G form a coclique in Γ (G), but this coclique need not be maximal. In this paper we determine when the intransitive maximal subgroups of Sn and An are maximal cocliques in the generating graph. In addition, we prove a conjecture of Cameron, Lucchini, and Roney-Dougal in the case of G = An and Sn, when n is prime and n ≠ qd-1/q-1 for all prime powers q and d ≥ 2. Namely, we show that two elements of G have identical sets of neighbours in Γ (G) if and only if they belong to exactly the same maximal subgroups.
dc.relation.ispartofCombinatorial Theoryen
dc.rightsCopyright © 2022 by the author(s). This work is made available under the terms of a Creative Commons Attribution License, available at
dc.subjectGenerating graphen
dc.subjectAlternating groupsen
dc.subjectSymmetric groupsen
dc.subjectQA Mathematicsen
dc.titleMaximal cocliques in the generating graphs of the alternating and symmetric groupsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.contributor.institutionUniversity of St Andrews. St Andrews GAP Centreen
dc.description.statusPeer revieweden

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