On localizations of torsion abelian groups

• Autorzy: José L. Rodríguez , Jérôme Scherer , Lutz Strüngmann
• Języki publikacji: EN

Abstrakty

EN

As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of LT is bounded by $|T|^{ℵ₀}$ 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.

Kategorie tematyczne

• 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
• 20F06: Cancellation theory; application of van Kampen diagrams
• 20K20: Torsion-free groups, infinite rank
• 20K40: Homological and categorical methods
• 20F28: Automorphism groups of groups
• 20E36: Automorphisms of infinite groups [For automorphisms of finite groups, see ]
• 14F35: Homotopy theory; fundamental groups
• 20E32: Simple groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 183
• Numer: 2
• Strony: 123-138

Daty

wydano

2004

Twórcy

autor

José L. Rodríguez

• Área de Geometría y Topología, CITE III, Universidad de Almería, E-04120 Almería, Spain

autor

Jérôme Scherer

• Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain

autor

Lutz Strüngmann

• Department of Mathematics, University of Duisburg-Essen, 45117 Essen, Germany

Identyfikatory

DOI

10.4064/fm183-2-4