The torsion of a group is the set
A group is said to be torsion-free if , i.e. the torsion consists only of the identity element.
If is abelian (or, more generally, locally nilpotent) then is a subgroup (the torsion subgroup) of . Whenever is a subgroup of , then it is fully invariant and is torsion-free.
Example 1 (Torsion of a finite group)
For any finite group , .
Example 2 (Torsion of the circle group)
The torsion of the circle group is .
|Date of creation||2013-03-22 13:21:38|
|Last modified on||2013-03-22 13:21:38|
|Last modified by||mhale (572)|