‘Finitely presented monoids with linear Dehn function need not have regular cross-sections’
[with V. Maltcev]
Semigroup Forum, 88, no. 2 (2014), pp. 300–315.
DOI: 10.1007/s00233-013-9531-6. MR: 3189098. ZBL: 1300.20057.

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 the fact that finitely presented groups with linear Dehn function always have regular cross-sections.