Completely decomposable pure subgroups of completely decomposable Abelian groups
type: Item
instance of: scholarly article
title: Completely decomposable pure subgroups of completely decomposable Abelian groups
zbMATH Open document ID: 0832.20078
author: G. Viljoen
author: László Fuchs
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1996-02-25T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108344
review text: The authors investigate conditions under which pure subgroups of completely decomposable groups are again completely decomposable. For a pure subgroup \(A\) of a completely decomposable group \(B\), the following are equivalent: (a) \(A\) is completely decomposable; (b) there is an \(\aleph_0\)-prebalanced chain \(\{A_\sigma\}\) from \(A\) to \(B\) with countable factors such that, for each member \(A_\sigma\) of the chain, every countable subgroup of \(A_\sigma\) can be embedded in a countable completely decomposable pure subgroup of \(A_\sigma\); (c) there is a continuous well-ordered ascending chain of pure subgroups \(\{A_\sigma\}\) from \(A\) to \(B\) with countable factors such that each member \(A_\sigma\) is completely decomposable; (d) there is a \(G(\aleph_0)\)-family of completely decomposable pure subgroups of \(B\) over \(A\) (Th. 6).
Mathematics Subject Classification ID: 20K20
Mathematics Subject Classification ID: 20K27
Mathematics Subject Classification ID: 20K25
zbMATH DE Number: 763293
zbMATH Keywords: prebalanced chains
zbMATH Keywords: pure subgroups
zbMATH Keywords: completely decomposable groups
zbMATH Keywords: countable factors
zbMATH Keywords: completely decomposable pure subgroups
zbMATH Keywords: ascending chains of pure subgroups
reviewed by: Ladislav Bican
MaRDI profile type: Publication
cites work: Completely decomposable abelian groups any pure subgroup of which is completely decomposable
cites work: Completely decomposable abelian groups any regular subgroup of which is completely decomposable
cites work: On abelian groups by which balanced extensions of a rational group split
cites work: Subgroups of butler groups
cites work: Separable pure subgroups of completely decomposable torsion-free abelian groups
cites work: Butler groups of infinite rank
cites work: Torsion Free Groups
cites work: Q3946349
cites work: On Completely Decomposable Groups
description: scientific article; zbMATH DE number 763293