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If There is an Exactly λ-Free Abelian Group Then There is an Exactly λ-Separable one in λ

Saharon Shelah
The Journal of Symbolic Logic
Vol. 61, No. 4 (Dec., 1996), pp. 1261-1278
DOI: 10.2307/2275815
Stable URL: http://www.jstor.org/stable/2275815
Page Count: 18
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If There is an Exactly λ-Free Abelian Group Then There is an Exactly λ-Separable one in λ
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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 [2], p. 453. There, in pp. 241-242, this is discussed and proved in some cases. The existence of strongly λ-free ones was proved earlier by the criteria in [5] and [3]. We can apply a similar proof to a large class of other varieties in particular to the variety of (non-commutative) groups.

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