Free subgroups with torsion quotients and profinite subgroups with torus quotients
type: Item
instance of: scholarly article
title: Free subgroups with torsion quotients and profinite subgroups with torus quotients
zbMATH Open document ID: 1504.22005
DOI: 10.4171/RSMUP/64
author: Wayne Lewis
author: Peter Loth
author: Adolf Mader
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2021-07-02T00:00:00Z
review text: All groups are abelian. The authors study the full free subgroups \(F\) of a torsion free abelian group of finite rank \(A\) i.e., the free subgroups of \(A\) with torsion quotient. Let \(\mathfrak{F}(A)\) denote the set of all full free subgroups of \(A\). It is obtained numerous properties of groups which belong to the class \(\mathfrak{F}(A)\). A protorus is a compact, connected, finite dimensional topological group. If \(G\) is a protorus then compact totally disconnected subgroups \(\Delta\) of \(G\) such that \(G/\Delta\) is a torus is called \(\delta\)-subgroup. \(\delta\)-subgroups are essential ingredients in the important Resolution Theorem a description of compact groups. The authors receive the characterization \(\delta\)-subgroups from the properties of full free subgroups with the help of Pontryagin's duality. The authors introduce a new topology on a torsion free abelian group \(A\) by the set \(\mathfrak{F}(A)\) (the free or \(\mathfrak{F}\)-topology of \(A\)). It is received some results about completion in this topology. The authors introduce by \(\delta\)-subgroups the new topology on a protorus (\(\mathcal{D}\)-topology) and they explore it.
Mathematics Subject Classification ID: 22C05
Mathematics Subject Classification ID: 20K15
Mathematics Subject Classification ID: 22B05
zbMATH DE Number: 7367416
zbMATH Keywords: torsion-free abelian group
zbMATH Keywords: finite rank
zbMATH Keywords: full free subgroup
zbMATH Keywords: Pontryagin duality
zbMATH Keywords: compact abelian group
zbMATH Keywords: totally disconnected
zbMATH Keywords: profinite
zbMATH Keywords: torus quotient
zbMATH Keywords: resolution theorem
reviewed by: Nikolay I. Kryuchkov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/rsmup/64
OpenAlex ID: W3111017874
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description: scientific article; zbMATH DE number 7367416