An abelian group $A$ is *cotorsion* provided that whenever $A \leq G$ with $G$ abelian and $G/A$ is
torsion-free, we have $G \cong A \oplus B$ for some $B \leq G$. An abelian group $A$ is
*cotorsion-free* if it contains no non-trivial cotorsion subgroup.

It seems that $\mathbb{Z}^{\omega}$ is cotorsion-free.

- What about an uncountable direct product like $\mathbb{Z}^{\mathfrak{c}}$? Is this group cotorsion-free?
- More generally, if $G_i$, $i \in I$ are slender abelian groups, must $\prod_{i\in I}G_i$ be cotorsion-free?