# Cotorsion group

In 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 ${\displaystyle M}$, this says that ${\displaystyle Ext(F,M)=0}$ for all torsion-free groups ${\displaystyle F}$. It suffices to check the condition for ${\displaystyle F}$ the group of rational numbers.