Small Semigroups Generating Varieties with Continuum Many Subvarieties
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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.
KeywordsSemigroups Monoids Varieties Finitely based Hereditarily finitely based
Mathematics Subject Classifications (2000)20M07 08B15
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- 12.Lee, E.W.H., Li, J.R.: Minimal non-finitely based monoids. (submitted)Google Scholar
- 13.Lee, E.W.H., Volkov, M.V.: Limit varieties generated by completely 0-simple semigroups. (submitted)Google Scholar
- 14.Murskiĭ, V.L.: The existence in the three-valued logic of a closed class with a finite basis having no finite complete system of identities. Sov. Math., Dokl. 6, 1020–1024 (1965); Translation of Dokl. Akad. Nauk SSSR 163, 815–818 (1965)Google Scholar
- 25.Sloane, N.J.A.: The On-line Encyclopedia of Integer Sequences. Published electronically at http://www.research.att.com/~njas/sequences