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arXiv · 2405.20197

A collection of cancellative, singly aligned, non-embeddable monoids

Milo Edwardes·Daniel Heath
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Abstract

By classical results of Malcev, cancellative monoids need not be group-embeddable. In this paper, we describe and give presentations for and study an infinite family $\mathcal{M}_n$ of cancellative monoids which are not group-embeddable, originating from Malcev's original work. We show that $\mathcal{M}_n$ is singly aligned for $n \geq 2$, owing to applications in the study of $\mathrm{C}^*$-algebras by Brix, Bruce and Dor-On. We finish by showing that $\mathcal{M}_1$ is not singly aligned, but is $2$-aligned.

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Milo Edwardes, Daniel Heath. 2024-05-30. A collection of cancellative, singly aligned, non-embeddable monoids. https://doi.org/10.1007/s00233-025-10509-2

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