Almost-free groups in varieties with torsion
type: Item
instance of: scholarly article
title: Almost-free groups in varieties with torsion
zbMATH Open document ID: 0625.20022
DOI: 10.1016/0021-8693(87)90130-X
author: Alun Lloyd Pope
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: A group G in a variety V of groups is said to be almost free in V if every subgroup of G which can be generated by fewer elements than the cardinality of G is contained in a V-free subgroup of G. In an earlier paper [J. Algebra 91, 36-52 (1984; Zbl 0569.20020)], the author showed that in every torsion-free variety V there is a non-free almost free group of cardinality \(\aleph_ n\) for each positive integer n. Here the same result is established for certain other varieties which may have torsion, namely those varieties which contain some finite non-abelian simple group.
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E05
zbMATH DE Number: 4014987
zbMATH Keywords: varieties of groups
zbMATH Keywords: filtered presentations
zbMATH Keywords: V-free subgroup
zbMATH Keywords: non-free almost free group
reviewed by: Roger M. Bryant
MaRDI profile type: Publication
cites work: Almost free groups in varieties
full work available at URL: 0021-8693(87)90130-x
OpenAlex ID: W2000415566
description: scientific article; zbMATH DE number 4014987