Irreducibility of certain pseudovarieties¹

¹The two first authors were partially supported by NSF Grant DMS920381. Part of this work was done while the second author was an invited Professor at the Université Paris-VI.All three authors were partially supported by the Center for Communication and Information Science of the University of Nebraska.

Abstract

We prove that the pseudovarieties of all finite semigroups, and of all aperiodic finii e 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 th.it H is closed under semidirect product.

¹The two first authors were partially supported by NSF Grant DMS920381. Part of this work was done while the second author was an invited Professor at the Université Paris-VI.All three authors were partially supported by the Center for Communication and Information Science of the University of Nebraska.

¹The two first authors were partially supported by NSF Grant DMS920381. Part of this work was done while the second author was an invited Professor at the Université Paris-VI.All three authors were partially supported by the Center for Communication and Information Science of the University of Nebraska.

Notes

¹The two first authors were partially supported by NSF Grant DMS920381. Part of this work was done while the second author was an invited Professor at the Université Paris-VI.All three authors were partially supported by the Center for Communication and Information Science of the University of Nebraska.