The free spectra of semigroup varieties - simple semigroups
by
Kamilla Kátai-Urbán
Bolyai Institute, University of Szeged
Coauthors: Csaba Szabó (Eötvös Loránd University, Budapest)

The free spectrum of a variety is the sequence of cardinalities of the size of the free algebras. By the Higman-Neumann theorem the free spectrum of a group variety generated by a simple group G is exponential if G is nilpotent and doubly-exponential otherwise. The completely 0-simple semigroups are such building blocks for semigroups, as simple groups are for groups. In the talk, we look for the free spectra of the varieties generated by a finite completely 0-simple semigroup. We describe the structure of these semigroups and analyze the terms over them.

Date received: May 5, 2008