torsion
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 .
Title | torsion |
Canonical name | Torsion |
Date of creation | 2013-03-22 13:21:38 |
Last modified on | 2013-03-22 13:21:38 |
Owner | mhale (572) |
Last modified by | mhale (572) |
Numerical id | 8 |
Author | mhale (572) |
Entry type | Definition |
Classification | msc 20K10 |
Synonym | group torsion |
Related topic | PeriodicGroup |
Defines | torsion-free |
Defines | torsion group |
Defines | torsion subgroup |
Defines | torsion free |