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In mathematics, in the realm of abelian group theory, an abelian group is said to be cotorsion if every extension of it by a torsion-free group splits. If the group is C, this is equivalent to asserting that Ext(G,C)=0 for all torsion-free groups G. It suffices to check the condition for G being the group of rational numbers.

Some properties of cotorsion groups:

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