A unified syntactical approach to theorems of Putcha, Margolis, and Straubing on finite power semigroups
type: Item
instance of: scholarly article
title: A unified syntactical approach to theorems of Putcha, Margolis, and Straubing on finite power semigroups
zbMATH Open document ID: 0765.20029
DOI: 10.1007/BF02573549
published in: Semigroup Forum
publication date: 1993-04-01T00:00:00Z
full work available at URL: https://eudml.org/doc/135215
review text: Short direct proofs are given of various results on (finite) power semigroups based on pseudoidentity manipulation. For instance, the pseudovariety generated by all power semigroups, the regular \({\mathcal J}\)- classes of which are aperiodic subsemigroups, is contained in a particular pseudovariety \(CJ\) (Straubing), the power semigroups of a pseudovariety \(V\) generate the pseudovariety of all semigroups if and only \(V\) contains the five-element combinatorial Brandt semigroup (Margolis), and if a simple group \(G\) divides the power semigroup of a finite semigroup \(S\), the regular \({\mathcal J}\)-classes of which form a subsemigroup, then \(G\) divides \(S\) (Putcha).
reviewed by: Peter M. Higgins
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 08C15
zbMATH DE Number: 150436
zbMATH Keywords: pseudoidentity
zbMATH Keywords: pseudovariety
zbMATH Keywords: power semigroups
zbMATH Keywords: regular \({\mathcal J}\)- classes
zbMATH Keywords: five-element combinatorial Brandt semigroup
zbMATH Keywords: finite semigroups
author: Jorge Almeida
MaRDI profile type: Publication
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OpenAlex ID: W2039231135
description: scientific article; zbMATH DE number 150436