Let $G$ and $H$ be groups with identity elements $1_G$ and $1_H$, respectively. Let $\varphi: G \to H$ be a [group isomorphism](/page/Group%20Isomorphism), and let $g \in G$. Then
where $\operatorname{ord}(x)$ denotes the least positive integer $n$ such that $x^n$ is the identity element, if such an integer exists, and denotes $\infty$ otherwise.