# Sh:772

- Shelah, S., & Strüngmann, L. H. (2003).
*Kulikov’s problem on universal torsion-free abelian groups*. J. London Math. Soc. (2),**67**(3), 626–642. arXiv: math/0112253 DOI: 10.1112/S0024610703004216 MR: 1967696 -
Abstract:

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 {\rm 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 {\rm 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. - published version (17p)

Bib entry

@article{Sh:772, author = {Shelah, Saharon and Str{\"u}ngmann, Lutz H.}, title = {{Kulikov's problem on universal torsion-free abelian groups}}, journal = {J. London Math. Soc. (2)}, fjournal = {Journal of the London Mathematical Society. Second Series}, volume = {67}, number = {3}, year = {2003}, pages = {626--642}, issn = {0024-6107}, doi = {10.1112/S0024610703004216}, mrclass = {20K40 (20K20 20K35)}, mrnumber = {1967696}, mrreviewer = {Simone L. Wallutis}, doi = {10.1112/S0024610703004216}, note = {\href{https://arxiv.org/abs/math/0112253}{arXiv: math/0112253}}, arxiv_number = {math/0112253} }