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Permutation-based presentations for Brin's higher-dimensional Thompson groups nV
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dc.contributor.author | Quick, Martyn | |
dc.date.accessioned | 2022-12-19T12:30:01Z | |
dc.date.available | 2022-12-19T12:30:01Z | |
dc.date.issued | 2024-02-01 | |
dc.identifier | 257355381 | |
dc.identifier | f05c88bc-021e-4d15-bdc7-d3d49a8b2a8e | |
dc.identifier | 000884207800001 | |
dc.identifier | 85183897804 | |
dc.identifier.citation | Quick , M 2024 , ' Permutation-based presentations for Brin's higher-dimensional Thompson groups n V ' , Journal of the Australian Mathematical Society , vol. 116 , no. 1 , pp. 39-67 . https://doi.org/10.1017/S1446788722000210 | en |
dc.identifier.issn | 1446-7887 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/1901.04409v1 | |
dc.identifier.other | ORCID: /0000-0002-5227-2994/work/123196873 | |
dc.identifier.uri | https://hdl.handle.net/10023/26623 | |
dc.description.abstract | The higher-dimensional Thompson groups nV , for n⩾2 , were introduced by Brin [‘Presentations of higher dimensional Thompson groups’, J. Algebra284 (2005), 520–558]. We provide new presentations for each of these infinite simple groups. The first is an infinite presentation, analogous to the Coxeter presentation for the finite symmetric group, with generating set equal to the set of transpositions in nV and reflecting the self-similar structure of n-dimensional Cantor space. We then exploit this infinite presentation to produce further finite presentations that are considerably smaller than those previously known. | |
dc.format.extent | 29 | |
dc.format.extent | 457185 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of the Australian Mathematical Society | en |
dc.subject | Presentations | en |
dc.subject | Thompson's groups | en |
dc.subject | Higher-dimensional Thompson's group | en |
dc.subject | Simple groups | en |
dc.subject | Generators and relations | en |
dc.subject | Permutations | en |
dc.subject | Transpositions | en |
dc.subject | Baker's map | en |
dc.subject | Cantor space | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | MCC | en |
dc.subject.lcc | QA | en |
dc.title | Permutation-based presentations for Brin's higher-dimensional Thompson groups nV | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1017/S1446788722000210 | |
dc.description.status | Peer reviewed | en |
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