On localizations of torsion abelian groups

Volume 183 / 2004

José L. Rodríguez, Jérôme Scherer, Lutz Strüngmann Fundamenta Mathematicae 183 (2004), 123-138 MSC: Primary 20E06, 20E32, 20E36, 20F06, 20F28, 20K40, 20K20; Secondary 14F35. DOI: 10.4064/fm183-2-4


As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of $LT$ is bounded by $|T|^{\aleph_0}$ whenever $T$ is torsion abelian and $L$ is a localization functor. In this paper we study localizations of torsion abelian groups and investigate new examples. In particular we prove that the structure of $LT$ is determined by the structure of the localization of the primary components of $T$ in many cases. Furthermore, we completely characterize the relationship between localizations of abelian $p$-groups and their basic subgroups.


  • José L. RodríguezÁrea de Geometría y Topología, CITE III
    Universidad de Almería
    E-04120 Almería, Spain
  • Jérôme SchererDepartament de Matemàtiques
    Universitat Autònoma de Barcelona
    E-08193 Bellaterra, Spain
  • Lutz StrüngmannDepartment of Mathematics
    University of Duisburg-Essen
    45117 Essen, Germany

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