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On finite simple semigroups

Published online by Cambridge University Press:  20 January 2009

Jorge Almeida
Jorge Almeida
Affiliation:
Inic-Centro de MatemáticaFaculdade de CiênciasUniversidade do Porto4000 PortoPortugal
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Implicit operations (new operations commuting with all old homomorphisms) on pseudovarieties have been shown to play an important role in the study of these classes. They may be used to axiomatize sub-pseudovariaties and to describe recognizable subsets of (relatively) free objects. This paper presents a case study for the pseudovariety CS consisting of all finite simple semigroups. Based on a result of profinite group theory, a structural description of semigroups of implicit operations on finite simple semigroups is used to deduce that CS is join-irreducible.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 2 , June 1991 , pp. 205 - 215
Copyright
Copyright © Edinburgh Mathematical Society 1991

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