Torsion-free group

Definition
A group is said to be torsion-free or aperiodic if it has no non-identity periodic element, or equivalently, if there is no non-identity element of finite order.

(The term aperiodic is sometimes also used with slightly different meanings, so torsion-free is the more unambiguous term).

Stronger properties

 * Weaker than::Free group
 * Weaker than::Group of finite cohomological dimension

Prime-parametrized version

 * Torsion-free group for a set of primes: Given a set of primes $$\pi$$, a $$\pi$$-torsion-free group is a group that has no element of order $$p$$ for any $$p \in \pi$$.