Kulikov's problem on universal torsion-free abelian groups revisited

Saharon Shelah; Lutz Strüngmann

doi:10.1112/blms/bdr055

Kulikov's problem on universal torsion-free abelian groups revisited

Saharon Shelah^*, Lutz Strüngmann

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let T be a torsion abelian group. We consider the class of all torsion-free abelian groups G satisfying Ext(G,T)=0 and search for -universal objects in this class. We show that, for certain T there is no -universal group. However, for uncountable cardinals there is always a -universal group if we assume (V=L). Together with results by the second author this solves completely a problem by Kulikov.

Original language	English
Pages (from-to)	1198-1204
Number of pages	7
Journal	Bulletin of the London Mathematical Society
Volume	43
Issue number	6
DOIs	https://doi.org/10.1112/blms/bdr055
State	Published - Dec 2011

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abstract = "Let T be a torsion abelian group. We consider the class of all torsion-free abelian groups G satisfying Ext(G,T)=0 and search for -universal objects in this class. We show that, for certain T there is no -universal group. However, for uncountable cardinals there is always a -universal group if we assume (V=L). Together with results by the second author this solves completely a problem by Kulikov.",

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Kulikov's problem on universal torsion-free abelian groups revisited

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