Quasi-isometry and finite presentations of left cancellative monoids
Group Theory
2012-04-12 v1 Rings and Algebras
Abstract
We show that being finitely presentable and being finitely presentable with solvable word problem are quasi-isometry invariants of finitely generated left cancellative monoids. Our main tool is an elementary, but useful, geometric characterisation of finite presentability for left cancellative monoids. We also give examples to show that this characterisation does not extend to monoids in general, and indeed that properties such as solvable word problem are not isometry invariants for general monoids.
Keywords
Cite
@article{arxiv.1204.2384,
title = {Quasi-isometry and finite presentations of left cancellative monoids},
author = {Robert D. Gray and Mark Kambites},
journal= {arXiv preprint arXiv:1204.2384},
year = {2012}
}
Comments
13 pages