On localizations of torsion abelian groups
Tom 183 / 2004
Fundamenta Mathematicae 183 (2004), 123-138
MSC: Primary 20E06, 20E32, 20E36, 20F06, 20F28, 20K40,
20K20; Secondary 14F35.
DOI: 10.4064/fm183-2-4
Streszczenie
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.
