The semigroup inclusion class $\mathbf{ I} = [xyxy = xy; xyz \in \{ xywz, xuyz\}]$ is the union of two maximal subvarieties of $\mathbf{ GRB} = [xyzxy=xy]$. Monzo ( arXiv:1411.4860 ) described the lattice of semigroup inclusion classes below $\mathbf{ I}$ and asked if $\mathbf{ I}$ is covered by $\mathbf{ GRB}$. Our main result is a characterization of $\mathbf{ I}$ which makes it easy to answer Monzo's question in the negative.
Categories: math.RA math.GR