If G is a group, then the torsion elements Tor(G) of G (also called the torsion of G) are defined to be the set of elements g in G such that g^n = e for some natural number n, where e is the identity element of the group G. In the case that G is Abelian, Tor(G) is a subgroup and is called the torsion subgroup of G. If Tor(G) consists only of the identity element, the group G is called torsion-free.

Abelian group | free Abelian group | group | identity element