Non-finitely related and finitely related monoids

Abstract

We transform the method of Glasson into a sufficient condition under which a monoid is non-finitely related, add a new member to the collection of interlocking word-patterns, and use it to show that the monoid $M(a{b}^{2}a,a^2{b}^2)$ is non-finitely related. We also give a sufficient condition under which a monoid is finitely related and use it show that $M(a^2{b}^2)$ is finitely related. Together with the results of Glasson this completes the description of all finitely related monoids among the monoids of the form $M(W)$ where every word $\mathbf{u}\in W$ depends on two variables and every variable occurs twice in $\mathbf{u}$.

arXiv commentChanged title. To appear in Semigroup Forum