order

《Abstract Algebra》 · 第 20 页 · Section 1.1「Basic Axioms and Examples」，Definition

For $G$ a group and $x\in G$ define the order of $x$ to be the smallest positive integer $n$ such that $x^n=1$, and denote this integer by $|x|$. In this case $x$ is said to be of order $n$. If no positive power of $x$ is the identity, the order of $x$ is defined to be infinity and $x$ is said to be of infinite order.