Some pseudovariety joins involving the pseudovariety of finite groups
type: Item
instance of: scholarly article
title: Some pseudovariety joins involving the pseudovariety of finite groups
zbMATH Open document ID: 0633.20040
DOI: 10.1007/BF02573123
author: Jorge Almeida
published in: Semigroup Forum
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134914
review text: Let ZE, IE, G, Com, and N denote respectively the pseudovarieties of (all finite) semigroups in which idempotents are central, semigroups which are nilpotent extensions of groups, groups, commutative semigroups, and nilpotent semigroups. It is shown that \(G\vee Com=ZE\) and \(G\vee (Com\cap N)=IE\), and a sublattice of the lattice of all pseudovarieties of semigroups containing all the above pseudovarieties is completely described. This settles some decidability conjectures proposed by Rhodes. The basic tools in the proofs are Reiterman's characterization of pseudovarieties in terms of pseudoidentities and the semigroup of n-ary implicit operations on ZE, whose structure was described by the author and Azevedo.
reviewed by: Jorge Almeida
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08C15
zbMATH DE Number: 4029841
zbMATH Keywords: lattice of pseudovarieties of semigroups
zbMATH Keywords: nilpotent extensions of groups
zbMATH Keywords: commutative semigroups
zbMATH Keywords: nilpotent semigroups
zbMATH Keywords: pseudoidentities
MaRDI profile type: Publication
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OpenAlex ID: W1971939398
description: scientific article; zbMATH DE number 4029841