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 |
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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 | |
State | Published - 10 Dec 2008 |
Keywords
- Abelian group
- Divisible
- Free
- Gamma invariant
- Stationary set