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Torsion (Group Theory)

If $G$ is a Group, then the torsion elements $\mathop{\rm Tor}(G)$ 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, $\mathop{\rm Tor}(G)$ is a Subgroup and is called the torsion subgroup of $G$. If $\mathop{\rm Tor}(G)$ consists only of the Identity Element, the Group $G$ is called torsion-free.

See also Abelian Group, Group, Identity Element

© 1996-9 Eric W. Weisstein