Torsion-free abelian group
= Torsion-free abelian group
{title2=$na=0,\ n\ne0\Rightarrow a=0$}
An abelian group in which no nonzero element has finite order. <Free abelian groups> are torsion-free, but torsion-free groups need not be free, as the additive rationals show. This algebraic meaning differs from the torsion-free connection in differential geometry.