On the Baker's map and the Simplicity of the Higher Dimensional Thompson Groups nV

Abstract

We show that the baker's map is a product of transpositions (particularly pleasant involutions), and conclude from this that an existing very short proof of the simplicity of Thompson's group V applies with equal brevity to the higher dimensional Thompson groups nV.

3 pages

References in corpus (2)

• Higher Dimensional Thompson Groups
• Presentations of higher dimensional Thompson groups

Cited by in corpus (13)

• Twisted Brin-Thompson groups
• Isomorphisms of Brin-Higman-Thompson groups
• Diffeomorphisms groups of tame Cantor sets and Thompson-like groups
• Infinite $\frac{3}{2}$-generated groups
• Etale groupoids arising from products of shifts of finite type
• Presentations for the higher dimensional Thompson's groups nV
• The word problem of the Brin-Higman-Thompson groups
• Permutation-based presentations for Brin's higher-dimensional Thompson groups $nV$
• Higher dimensional Thompson groups have Serre's property FA
• A monoid version of the Brin-Higman-Thompson groups
• The word problem of the Brin-Thompson group is coNP-complete
• Divergence functions of higher-dimensional Thompson's groups
• Towards computing the rational homology and assembly maps of generalised Thompson groups