Order of a group element (reviewed)

The order of an element $g$ in a multiplicative group $G$ is the least positive integer $n$ such that $g^n$ is the identity element of $G$, if such an integer exist, and is $\infty$ otherwise. In an additive group, the order of $g$ is the least positive integer $n$ such that $ng=0$. In both cases, the order of $g$ is also equal to the cardinality of the cyclic subgroup it generates.