# Sh:521

- Shelah, S. (1996).
*If there is an exactly \lambda-free abelian group then there is an exactly \lambda-separable one in \lambda*. J. Symbolic Logic,**61**(4), 1261–1278. arXiv: math/9503226 DOI: 10.2307/2275815 MR: 1456106 -
Abstract:

We give a solution stated in the title to problem 3 of part 1 of the problems listed in the book of Eklof and Mekler [EM],(p.453). There, in pp. 241-242, this is discussed and proved in some cases. The existence of strongly \lambda-free ones was proved earlier by the criteria in [Sh:161] in [MkSh:251]. We can apply a similar proof to a large class of other varieties in particular to the variety of (non-commutative) groups. - published version (19p)

Bib entry

@article{Sh:521, author = {Shelah, Saharon}, title = {{If there is an exactly $\lambda$-free abelian group then there is an exactly $\lambda$-separable one in $\lambda$}}, journal = {J. Symbolic Logic}, fjournal = {The Journal of Symbolic Logic}, volume = {61}, number = {4}, year = {1996}, pages = {1261--1278}, issn = {0022-4812}, doi = {10.2307/2275815}, mrclass = {20K20 (03E75 08B20)}, mrnumber = {1456106}, mrreviewer = {Milan Grulovi\'c}, doi = {10.2307/2275815}, note = {\href{https://arxiv.org/abs/math/9503226}{arXiv: math/9503226}}, arxiv_number = {math/9503226} }