The word problem of the Brin-Higman-Thompson groups

Abstract

We show that the word problem of the Brin-Higman-Thompson group $n{G}_{k,1}$ is {\sf coNP}-complete for all $n\ge 2$ and all $k\ge 2$. For this we prove that $n{G}_{k,1}$ is finitely generated, and that $n{G}_{k,1}$ contains a subgroup of $2G_{2,1}$ that can represent bijective circuits. We also show that for all $n\ge 1$ and $k\ge 2$: \ If $K=1+(k-1)N$ for some $N\ge 1$, then $n{G}_{K,1}\le n{G}_{k,1}$. In particular, $n{G}_{K,1}\le n{G}_{2,1}$ for all $K\ge 2$.

27 pages

References in corpus (2)

• Rigidity properties of full groups of pseudogroups over the Cantor set
• Permutation-based presentations for Brin's higher-dimensional Thompson groups $nV$

Cited by in corpus (2)

• A monoid version of the Brin-Higman-Thompson groups
• Evaluation problems for the Thompson group and the Brin-Thompson group, and their relation to the word problem