Permutation-based presentations for Brin's higher-dimensional Thompson groups $nV$

Abstract

The higher-dimensional Thompson groups $nV$, for $n\ge 2$, were introduced by Brin in 2005. 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.

23 pages, 2 figures, accepted for publication in J Austral Math Soc

Cited by in corpus (2)

• The word problem of the Brin-Higman-Thompson groups
• A Description of Aut(dVn) and Out(dVn) Using Transducers