Displaying similar documents to “ε-Kronecker and I₀ sets in abelian groups, III: interpolation by measures on small sets”

On localizations of torsion abelian groups

José L. Rodríguez, Jérôme Scherer, Lutz Strüngmann (2004)

Fundamenta Mathematicae

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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 | ℵ 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...

ε-Kronecker and I₀ sets in abelian groups, IV: interpolation by non-negative measures

Colin C. Graham, Kathryn E. Hare (2006)

Studia Mathematica

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A subset E of a discrete abelian group is a "Fatou-Zygmund interpolation set" (FZI₀ set) if every bounded Hermitian function on E is the restriction of the Fourier-Stieltjes transform of a discrete, non-negative measure. We show that every infinite subset of a discrete abelian group contains an FZI₀ set of the same cardinality (if the group is torsion free, a stronger interpolation property holds) and that ε-Kronecker sets are FZI₀ (with that stronger interpolation...

The automorphism groups and endomorphism rings of torsion-free abelian groups of rank two

M. Król

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CONTENTS§ 1. Introduction.......................................................................................................................................... 5§ 2. Definitions and lemmas................................................................................................................... 7§ 3. Theorem on the isomorphism of subdirect sums with the same kernels............................. 15§ 4. The group of automorphisms of a torsion-free abelian group of rank two................................