Quasi-isometry and finite presentations for left cancellative monoids

Robert Gray, M Kambites

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3 Citations (Scopus)


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 characterization of finite presentability for left cancellative monoids. We also give examples to show that this characterization does not extend to monoids in general, and indeed that properties such as solvable word problem are not isometry invariants for general monoids.
Original languageEnglish
Pages (from-to)1099-1114
Number of pages16
JournalInternational Journal of Algebra and Computation
Issue number5
Publication statusPublished - Aug 2013

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