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arXiv · 1302.0982

Monoids $\mathrm{Mon}\langle a,b:a^{\alpha}b^{\beta}a^{\gamma}b^{\delta}=b\rangle$ admit finite complete rewriting systems

Alan Cain·Victor Maltcev
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Abstract

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

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Alan Cain, Victor Maltcev. 2013-02-05. Monoids $\mathrm{Mon}\langle a,b:a^{\alpha}b^{\beta}a^{\gamma}b^{\delta}=b\rangle$ admit finite complete rewriting systems. https://arxiv.org/abs/1302.0982

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