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Jackson and Lee proved that certain six-element monoid generates ahereditarily finitely based variety $\mathbb E^1$ whose lattice of subvarietiescontains an infinite ascending chain. We identify syntactic monoids whichgenerate finitely generated subvarieties of $\mathbb E^1$ and show that one ofthese finite monoids together with certain seven-element monoid generates a newlimit variety.

Limit varieties generated by finite non-J-trivial aperiodic monoids