For several large classes of semigroups we provide a description of all semigroups which generate varieties with uncountably many subvarieties. These include the class of all Rees quotients of free monoids, the class of finite orthodox monoids, the class of monoids of index greater than two, and the class of finite inherently not finitely based semigroups. The first example of a finite, finitely based semigroup generating a variety with uncountably many subvarieties is presented and a number of related results are obtained. All varieties found with uncountably many subvarieties contain uncountable chains of subvarieties with the same ordering as the real numbers. © 2000 Academic Press.

Item Type:	Refereed Article
Research Division:	Mathematical Sciences
Research Group:	Pure Mathematics
Research Field:	Group Theory and Generalisations
Objective Division:	Expanding Knowledge
Objective Group:	Expanding Knowledge
Objective Field:	Expanding Knowledge in the Mathematical Sciences
Author:	Jackson, MG (Dr Marcel Jackson)
ID Code:	18702
Year Published:	2000
Web of Science® Times Cited:	29
Deposited By:	Mathematics
Deposited On:	2000-08-01
Last Modified:	2011-08-04
Downloads:	0