Uniquely Transitive Torsion-free Abelian Groups

2004/04/14 by Rüdiger Göbel, Saharon Shelah, Göbel, Rüdiger +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Rings, Modules, and Algebras #math.LO

paper · pdf · doi:10.48550/arxiv.math/0404259

published as in: {Rings, modules, algebras, and abelian groups} (2004) 271--290

arxiv created 2004/04/14 · arxiv updated 2009/12/01

Abstract

We will answer a question raised by Emmanuel Dror Farjoun concerning the existence of torsion-free abelian groups G such that for any ordered pair of pure elements there is a unique automorphism mapping the first element onto the second one. We will show the existence of such a group of cardinality lambda for any successor cardinal lambda=mu⁺ with mu=mu^aleph₀.

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