Basic subgroups and freeness, a counterexample

Andreas Blass; Saharon Shelah

doi:10.1515/9783110203035.63

Basic subgroups and freeness, a counterexample

Andreas Blass^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-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 language	English
Title of host publication	Models, Modules and Abelian Groups
Subtitle of host publication	In Memory of A. L. S. Corner
Publisher	Walter de Gruyter GmbH and Co. KG
Pages	63-73
Number of pages	11
ISBN (Print)	9783110194371
DOIs	https://doi.org/10.1515/9783110203035.63
State	Published - 10 Dec 2008

Keywords

Abelian group
Divisible
Free
Gamma invariant
Stationary set

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10.1515/9783110203035.63

Cite this

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Basic subgroups and freeness, a counterexample

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Keywords

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