Mathematics Faculty Articles

Title

Small Semigroups Generating Varieties with Continuum Many Subvarieties

Document Type

Article

Publication Date

3-2010

Publication Title

Order

Keywords

Semigroups, Monoids, Varieties, Finitely based, Hereditarily finitely based

ISSN

0167-8094

Volume

27

Issue/No.

1

First Page

83

Last Page

100

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.

Comments

Mathematics Subject Classifications (2000)

20M07

08B15

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.1007/s11083-010-9142-8

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Peer Reviewed

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