What is "torsion-free"

In mathematics, the term torsion-free may refer to several unrelated notions:

• In abstract algebra, a group is torsion-free if the only element of finite order is the identity.
• In abstract algebra, a torsion-free module is one with no nonzero torsion elements.
• In differential geometry, an affine connection is torsion-free if its torsion tensor vanishes.