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, Volume 27, Issue 1, pp 83–100 | Cite as

Small Semigroups Generating Varieties with Continuum Many Subvarieties

  • Charles C. Edmunds
  • Edmond W. H. Lee
  • Ken W. K. Lee
Article

Abstract

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.

Keywords

Semigroups Monoids Varieties Finitely based Hereditarily finitely based 

Mathematics Subject Classifications (2000)

20M07 08B15 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Charles C. Edmunds
    • 1
  • Edmond W. H. Lee
    • 2
  • Ken W. K. Lee
    • 3
  1. 1.Department of MathematicsMount Saint Vincent UniversityHalifaxCanada
  2. 2.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  3. 3.Department of Information SystemsCity University of Hong KongHong KongPeople’s Republic of China

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