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dc.contributor.authorCameron, Peter J.
dc.contributor.authorFreedman, Saul Daniel
dc.contributor.authorRoney-Dougal, Colva Mary
dc.identifier.citationCameron , P J , Freedman , S D & Roney-Dougal , C M 2021 , ' The non-commuting, non-generating graph of a nilpotent group ' , Electronic Journal of Combinatorics , vol. 28 , no. 1 , P1.16 .
dc.identifier.otherPURE: 271737536
dc.identifier.otherPURE UUID: 42700c0c-5e66-49d3-a8de-f2fd49eb9a00
dc.identifier.otherORCID: /0000-0002-0532-3349/work/87845459
dc.identifier.otherORCID: /0000-0003-3130-9505/work/87845623
dc.identifier.otherScopus: 85100181093
dc.identifier.otherWOS: 000619719200001
dc.descriptionFunding: UK ESPRC grant number EP/R014604/1, and partially supported by a grant from the Simons Foundation (PJC, CMR-D); ESPRC grant number EP/R014604/1, St Leonard’s International Doctoral Fees Scholarship, School of Mathematics & Statistics PhD Funding Scholarship at the University of St Andrews (SDF).en
dc.description.abstractFor a nilpotent group G, let nc(G) be the difference between the complement of the generating graph of G and the commuting graph of G, with vertices corresponding to central elements of G removed. That is, nc(G) has vertex set G \ Z(G), with two vertices adjacent if and only if they do not commute and do not generate G. Additionally, let nd(G) be the subgraph of nc(G) induced by its non-isolated vertices. We show that if nc(G) has an edge, then nd(G) is connected with diameter 2 or 3, with nc(G) = nd(G) in the diameter 3 case. In the infinite case, our results apply more generally, to any group with every maximal subgroup normal. When G is finite, we explore the relationship between the structures of G and nc(G) in more detail.
dc.relation.ispartofElectronic Journal of Combinatoricsen
dc.rightsCopyright © The authors. Released under the CC BY-ND license (International 4.0).en
dc.subjectQA Mathematicsen
dc.titleThe non-commuting, non-generating graph of a nilpotent groupen
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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