Kulikov's problem on universal torsion-free abelian groups

by Shelah and Struengmann. [ShSm:772]
J London Math Soc, 2003
Let T be an abelian group and lambda an uncountable regular cardinal. We consider the question of whether there is a lambda-universal group G^* among all torsion-free abelian groups G of cardinality less than or equal to lambda satisfying Ext (G,T)=0 . Here G^* is said to be lambda-universal for T if, whenever a torsion-free abelian group G of cardinality less than or equal to lambda satisfies Ext (G,T)=0, then there is an embedding of G into G^* . For large classes of abelian groups T and cardinals lambda it is shown that the answer is consistently no. In particular, for T torsion, this solves a problem of Kulikov.


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