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dc.contributor.authorBleak, Collin
dc.contributor.authorQuick, Martyn
dc.identifier.citationBleak , C & Quick , M 2017 , ' The infinite simple group V of Richard J. Thompson : presentations by permutations ' , Groups, Geometry, and Dynamics , vol. 11 , no. 4 , pp. 1401-1436 .
dc.identifier.otherPURE: 229627034
dc.identifier.otherPURE UUID: e675f4a8-7e08-492d-8123-38aa4381999b
dc.identifier.otherWOS: 000423287400010
dc.identifier.otherWOS: 000423287400010
dc.identifier.otherScopus: 85035076680
dc.identifier.otherORCID: /0000-0002-5227-2994/work/58054911
dc.identifier.otherORCID: /0000-0001-5790-1940/work/73701273
dc.description.abstractWe show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group V, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to transpositions.  This perspective provides an intuitive explanation towards the simplicity of V and also perhaps indicates a reason as to why it was one of the first discovered infinite finitely presented simple groups: it is (in some basic sense) a relative of the finite alternating groups.  We find a natural infinite presentation for V as a group generated by these "transpositions," which presentation bears comparison with Dehornoy's infinite presentation and which enables us to develop two small presentations for V: a human-interpretable presentation with three generators and eight relations, and a Tietze-derived presentation with two generators and seven relations.
dc.relation.ispartofGroups, Geometry, and Dynamicsen
dc.rights© 2017, EMS Publishing House. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectThompson's groupsen
dc.subjectSimple groupsen
dc.subjectGenerators and relationsen
dc.subjectQA Mathematicsen
dc.titleThe infinite simple group V of Richard J. Thompson : presentations by permutationsen
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.description.statusPeer revieweden

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