Torsion-free group

Summary

A torsion-free group is a group in which the identity is the only element of finite order. It is the opposite extreme to a torsion group. For an abelian group $A$, the quotient of $A$ by its torsion subgroup is torsion-free. A finitely generated torsion-free abelian group is a free abelian group $\Z^n$.