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dc.contributor.authorAshcroft, Calum
dc.contributor.authorRoney-Dougal, Colva Mary
dc.identifier.citationAshcroft , C & Roney-Dougal , C M 2020 , ' On random presentations with fixed relator length ' , Communications in Algebra , vol. Latest Articles .
dc.identifier.otherPURE: 263920476
dc.identifier.otherPURE UUID: 4ee1b194-a7ec-4ecb-af79-8950f68ac90b
dc.identifier.otherScopus: 85078286313
dc.identifier.otherORCID: /0000-0002-0532-3349/work/73700932
dc.identifier.otherWOS: 000508066000001
dc.description.abstractThe standard (n, k, d) model of random groups is a model where the relators are chosen randomly from the set of cyclically reduced words of length k on an n-element generating set. Gromov’s density model of random groups considers the case where n is fixed, and k tends to infinity. We instead fix k, and let n tend to infinity. We prove that for all k ≥ 2 at density d > 1/2 a random group in this model is trivial or cyclic of order two, whilst for d < 1 such 2 a random group is infinite and hyperbolic. In addition we show that for d < 1/k such a random k group is free, and that this threshold is sharp. These extend known results for the triangular (k = 3) and square (k = 4) models of random groups.
dc.relation.ispartofCommunications in Algebraen
dc.rightsCopyright © 2020 Taylor & Francis Group, LLC. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectFinitely-presented groupsen
dc.subjectRandom presentationsen
dc.subjectHyperbolic groupsen
dc.subjectRandom graphsen
dc.subjectQA Mathematicsen
dc.titleOn random presentations with fixed relator lengthen
dc.typeJournal articleen
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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