Irreducibility of certain pseudovarieties

S. Margolis, M. Sapir, P. Weil

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We prove that the pseudovarieties of all finite semigroups, and of all aperiodic finite semigroups are irreducible for join, for semidirect product and for Mal'cev product. In particular, these pseudovarieties do not admit maximal proper subpseudovarieties. More generally, analogous results are proved for the pseudovariety of all finite semigroups all of whose subgroups are in a fixed pseudovariety of groups H, provided that H is closed under semidirect product.

Original languageEnglish
Pages (from-to)779-792
Number of pages14
JournalCommunications in Algebra
Volume26
Issue number3
DOIs
StatePublished - 1998

Bibliographical note

Funding Information:
Nous prouvons que la pseudovaridtl de tous les semigroupes fin~se,t celle de tous 1.s semigroupes apdriodiques finis sont irrlductibles pour le sup, pour ie prodult sern (,I- rect et pour le produit de Mal'cev. En particulter, ces pseudovariktls n'adrnettent pas de sous-pseudovaridtl maximale propre. Des rlsultats analogues sent ktablis ~ l d s gendralement pour la pseudovariltd de tous les semigroupes finis dont les sous-groupes sont dans une pseudovariltl de groupes fixee H, pourvu que H sott fermCe par procatlit semidirect 'The two first authors were partially supported by NSF Grant DMS920381 Part of this v ork was done while the second author was an invited Professor at the Universit.4 Paris-\'I All three author!, ~verep artiall) supported by the Center for Communication and Information Science of the Univers~tyo f Uebraska.

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