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dc.contributor.authorBleak, Collin
dc.contributor.authorQuick, Martyn
dc.date.accessioned2017-12-08T12:30:08Z
dc.date.available2017-12-08T12:30:08Z
dc.date.issued2017
dc.identifier229627034
dc.identifiere675f4a8-7e08-492d-8123-38aa4381999b
dc.identifier000423287400010
dc.identifier000423287400010
dc.identifier85035076680
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 . https://doi.org/10.4171/GGD/433en
dc.identifier.issn1661-7207
dc.identifier.otherORCID: /0000-0002-5227-2994/work/58054911
dc.identifier.otherORCID: /0000-0001-5790-1940/work/73701273
dc.identifier.urihttps://hdl.handle.net/10023/12296
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.format.extent36
dc.format.extent398204
dc.language.isoeng
dc.relation.ispartofGroups, Geometry, and Dynamicsen
dc.subjectThompson's groupsen
dc.subjectSimple groupsen
dc.subjectPresentationsen
dc.subjectGenerators and relationsen
dc.subjectPermutationsen
dc.subjectTranspositionsen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectBDCen
dc.subjectR2Cen
dc.subject.lccQAen
dc.titleThe infinite simple group V of Richard J. Thompson : presentations by permutationsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doi10.4171/GGD/433
dc.description.statusPeer revieweden
dc.date.embargoedUntil2017-12-07
dc.identifier.urlhttp://arxiv.org/abs/1511.02123v1en
dc.identifier.grantnumberEP/H011978/1en


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