(University of St Andrews, UK)
20/06/2008 Sexta-feira, 20 de Junho de 2008, 14h30, Anfiteatro
The Bergman property for semigroups
In this talk, we will discuss the Bergman property for semigroups and the associated notions of cofinality and strong confinality. An uncountably infinite semigroup S is said to have the Bergman property if for all generating sets U there exists a number n so that every element of S is a product of at most n elements of U.
We will see that the semigroup of all mappings on an infinite set has the Bergman property but that its finitary power semigroup does not; the symmetric inverse semigroup on an infinite set and its finitary power semigroup have the Bergman property; the Baer-Levi semigroup does not have the Bergman property.