Small Semigroups Generating Varieties with Continuum Many Subvarieties
Semigroups, Monoids, Varieties, Finitely based, Hereditarily finitely based
The smallest finitely based semigroup currently known to generate a variety with continuum many subvarieties is of order seven. The present article introduces a new example of order six and comments on the possibility of the existence of a smaller example. It is shown that if such an example exists, then up to isomorphism and anti-isomorphism, it must be a unique monoid of order five.
Edmunds, Charles C.; Lee, Edmond W. H.; and Lee, Ken W.K., "Small Semigroups Generating Varieties with Continuum Many Subvarieties" (2010). Mathematics Faculty Articles. 153.