### If there is an exactly $\lambda$-free abelian group then there is an exactly $\lambda$-separable one

by Shelah. [Sh:521]

J Symbolic Logic, 1996

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.

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