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Finitely presented monoids with linear Dehn function need not have regular cross-sections

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Abstract

This paper shows that a finitely presented monoid with linear Dehn function need not have a regular cross-section, strengthening the previously-known result that such a monoid need not be presented by a finite complete string rewriting system, and contrasting with the fact that finitely presented groups with linear Dehn function always have regular cross-sections.

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Acknowledgements

The authors thank the anonymous referee for pointing out a flaw in an earlier proof of Lemma 9, and for making extensive comments and suggestions on improving the exposition.

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Authors and Affiliations

  1. Centro de Matemática, Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal

    Alan J. Cain

  2. Mathematics Department, Technion—Israel Institute of Technology, Haifa, 32000, Israel

    Victor Maltcev

Authors
  1. Alan J. Cain
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  2. Victor Maltcev
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Correspondence to Alan J. Cain.

Additional information

Communicated by Marcel Jackson.

During the research that led to the this paper, the first author was supported by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT (Fundação para a Ciência e a Tecnologia) under the project PEst-C/MAT/UI0144/2011 and through an FCT Ciência 2008 fellowship.

The research described in this paper has been included in the second author’s Ph.D. thesis [10, Sect. 7.2].

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Cain, A.J., Maltcev, V. Finitely presented monoids with linear Dehn function need not have regular cross-sections. Semigroup Forum 88, 300–315 (2014). https://doi.org/10.1007/s00233-013-9531-6

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  • DOI: https://doi.org/10.1007/s00233-013-9531-6

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