Characterization of group radicals with an application to Mal'cev products.
type: Item
instance of: scholarly article
title: Characterization of group radicals with an application to Mal'cev products.
zbMATH Open document ID: 1250.20046
author: Jorge Almeida
author: S. W. Margolis
author: Benjamin Steinberg
author: M. V. Volkov
published in: Illinois Journal of Mathematics
publication date: 2011-04-28T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ijm/1299679746
review text: The authors study Mal'cev products of the form \(\mathbf{LH}\circm\mathbf V\) where \(\mathbf{LH}\) is the pseudovariety of all finite semigroups whose local submonoids belong to a given pseudovariety \(\mathbf H\) of groups and \(\mathbf V\) is a pseudovariety of semigroups. In an earlier paper [Trans.\ Am.\ Math.\ Soc. 361, No. 3, 1429-1461 (2009; Zbl 1185.20058)], they have described such products in the case when \(\mathbf H\) either is trivial or coincides with the pseudovariety of all finite \(p\)-groups for some prime \(p\). Here the authors extend the description to the case when \(\mathbf H\) is a group pseudovariety being simultaneously a Fitting class (Theorem~5.2). They also show how to obtain a basis of pseudoidentities for \(\mathbf{LH}\circm\mathbf V\) from a basis of pseudoidentities for \(\mathbf V\) and a certain profinite characterization of the \(\mathbf H\)-radical (Theorem~6.1).
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 20M11
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 5882254
zbMATH Keywords: finite semigroups
zbMATH Keywords: semigroup pseudovarieties
zbMATH Keywords: group pseudovarieties
zbMATH Keywords: group radicals
zbMATH Keywords: Mal'cev products
zbMATH Keywords: Fitting pseudovarieties
zbMATH Keywords: bases of pseudoidentities
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5882254