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The infinite simple group V of Richard J. Thompson : presentations by permutations
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dc.contributor.author | Bleak, Collin | |
dc.contributor.author | Quick, Martyn | |
dc.date.accessioned | 2017-12-08T12:30:08Z | |
dc.date.available | 2017-12-08T12:30:08Z | |
dc.date.issued | 2017 | |
dc.identifier | 229627034 | |
dc.identifier | e675f4a8-7e08-492d-8123-38aa4381999b | |
dc.identifier | 000423287400010 | |
dc.identifier | 000423287400010 | |
dc.identifier | 85035076680 | |
dc.identifier.citation | Bleak , 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/433 | en |
dc.identifier.issn | 1661-7207 | |
dc.identifier.other | ORCID: /0000-0002-5227-2994/work/58054911 | |
dc.identifier.other | ORCID: /0000-0001-5790-1940/work/73701273 | |
dc.identifier.uri | https://hdl.handle.net/10023/12296 | |
dc.description.abstract | We 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.extent | 36 | |
dc.format.extent | 398204 | |
dc.language.iso | eng | |
dc.relation.ispartof | Groups, Geometry, and Dynamics | en |
dc.subject | Thompson's groups | en |
dc.subject | Simple groups | en |
dc.subject | Presentations | en |
dc.subject | Generators and relations | en |
dc.subject | Permutations | en |
dc.subject | Transpositions | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject.lcc | QA | en |
dc.title | The infinite simple group V of Richard J. Thompson : presentations by permutations | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.4171/GGD/433 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2017-12-07 | |
dc.identifier.url | http://arxiv.org/abs/1511.02123v1 | en |
dc.identifier.grantnumber | EP/H011978/1 | en |
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