A monoid version of the Brin-Higman-Thompson groups

Abstract

We generalize the Brin-Higman-Thompson groups $n{G}_{k,1}$ to monoids $n{M}_{k,1}$, for $n\ge 1$ and $k\ge 2$, by replacing bijections by partial functions. The monoid $n{M}_{k,1}$ has $n{G}_{k,1}$ as its group of units, and is congruence-simple. Moreover, $n{M}_{k,1}$ is finitely generated, and for $n\ge 2$ its word problem is {\sf coNP}-complete. We also present new results about higher-dimensional joinless codes.

26 pages

References in corpus (2)

• Circuits, coNP-completeness, and the groups of Richard Thompson
• The word problem of the Brin-Higman-Thompson groups

Cited by in corpus (1)

• Evaluation problems for the Thompson group and the Brin-Thompson group, and their relation to the word problem