Quasiidentities and direct wreaths of groups
type: Item
instance of: scholarly article
title: Quasiidentities and direct wreaths of groups
zbMATH Open document ID: 0579.20026
DOI: 10.1007/BF02071785
published in: Algebra and Logic
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187276
review text: The author continues his study of quasivarieties of groups, concentrating here on their connections with standard wreath products of groups, here called direct wreaths. For a given class of groups R, he defines qwr R to be the least quasivariety closed with respect to wreath products and containing R. The main results state that if G is a finite nontrivial group, a torsion-free group in a special class which includes cyclic groups and torsion free nilpotent groups or a group with one defining relator, then qwr G cannot be defined by a system of quasiidentities stable with respect to wreath products. The set of such quasivarieties has the cardinal of the continuum.
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 20E26
zbMATH DE Number: 3927195
zbMATH Keywords: quasivarieties of groups
zbMATH Keywords: standard wreath products
zbMATH Keywords: quasiidentities
author: Alexander Ivanovich Budkin
MaRDI profile type: Publication
cites work: Q3866275
cites work: Q4745992
cites work: Q4093507
cites work: Q5556574
cites work: Groups with one defining relator
cites work: Some results on one-relator groups
OpenAlex ID: W1991545448
description: scientific article; zbMATH DE number 3927195