‘Monoids $\mathrm{Mon}\langle a,b \mid a^\alpha b^\beta a^\gamma b^\delta = b\rangle$ admit finite complete rewriting systems’
[with V. Maltcev]
Technical report. Febuary 2013.
arXiv: 1302.0982.

Abstract

We prove that every monoid $\mathrm{Mon}\langle a,b\mid a^\alpha b^\beta a^\gamma b^\delta=b\rangle$ admits a finite complete rewriting system. Furthermore we prove that $\mathrm{Mon}\langle a,b \mid ab^2a^2b^2=b\rangle$ is non-hopfian, providing an example of a finitely presented non-residually finite monoid with linear Dehn function.