Basic subgroups and freeness, a counterexample

Andreas Blass*, Saharon Shelah

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations

Abstract

We construct a non-free but 1-separable, torsion-free abelian group G with a pure free subgroup B such that all subgroups of G disjoint from B are free and such that G/B is divisible. This answers a question of Irwin and shows that a theorem of Blass and Irwin cannot be strengthened so as to give an exact analog for torsion-free groups of a result proved for p-groups by Benabdallah and Irwin.

Original languageEnglish
Title of host publicationModels, Modules and Abelian Groups
Subtitle of host publicationIn Memory of A. L. S. Corner
PublisherWalter de Gruyter GmbH and Co. KG
Pages63-73
Number of pages11
ISBN (Print)9783110194371
DOIs
StatePublished - 10 Dec 2008

Keywords

  • Abelian group
  • Divisible
  • Free
  • Gamma invariant
  • Stationary set

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