Group Torsion

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.

See also

Abelian Group, Free Abelian Group, Group, Identity Element

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Cite this as:

Weisstein, Eric W. "Group Torsion." From MathWorld--A Wolfram Web Resource.

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