### Disjoint Non-Free Subgoups of Abelian Groups

by Blass and Shelah. [BsSh:870]

Quaderni di Matematica, 2006

Let G be an abelian group and let lambda be the smallest
rank of any group whose direct sum with a free group is isomorphic
to G . If lambda is uncountable, then G has lambda
pairwise disjoint, non-free subgroups. There is an example where
lambda is countably infinite and G does not have even two
disjoint, non-free subgroups.

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