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Small Semigroups Generating Varieties with Continuum Many Subvarieties

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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.

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Authors and Affiliations

  1. Department of Mathematics, Mount Saint Vincent University, Halifax, NS, B3M 2J6, Canada

    Charles C. Edmunds

  2. Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Edmond W. H. Lee

  3. Department of Information Systems, City University of Hong Kong, Hong Kong, People’s Republic of China

    Ken W. K. Lee

Authors
  1. Charles C. Edmunds
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  2. Edmond W. H. Lee
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  3. Ken W. K. Lee
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Correspondence to Edmond W. H. Lee.

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Dedicated to Professor Norman R. Reilly on the occasion of his 70th birthday.

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Edmunds, C.C., Lee, E.W.H. & Lee, K.W.K. Small Semigroups Generating Varieties with Continuum Many Subvarieties. Order 27, 83–100 (2010). https://doi.org/10.1007/s11083-010-9142-8

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  • DOI: https://doi.org/10.1007/s11083-010-9142-8

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