Permutation-based presentations for Brin's higher-dimensional Thompson groups nV
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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.
Quick , M 2022 , ' Permutation-based presentations for Brin's higher-dimensional Thompson groups n V ' , Journal of the Australian Mathematical Society , vol. FirstView . https://doi.org/10.1017/S1446788722000210
Journal of the Australian Mathematical Society
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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