For questions about torsion groups and their properties. A torsion group is a group in which every element has finite order.
A torsion group, also called a periodic group, is a group in which every element has finite order. That is, $G$ is a torsion group if for each $g \in G$ there is a nonnegative integer $n$ for which
$$g^n = e$$
where $e$ is the identity element of $G$.
Every finite group is torsion, but there are infinite torsion groups. The additive group of polynomials over a finite field is torsion, as is $\mathbb{Q} / \mathbb{Z}$ under addition. Note that a torsion group need not have finite exponent.
Reference: Torsion group.