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