# Cotorsion group

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 ${\displaystyle C}$, this is equivalent to asserting that ${\displaystyle Ext(G,C)=0}$ for all torsion-free groups ${\displaystyle G}$. It suffices to check the condition for ${\displaystyle G}$ being the group of rational numbers.