Definition:Orbit (Group Theory)/Length

Definition
Let $G$ be a group acting on a set $X$.

Let $x \in X$.

Let $\operatorname{Orb} \left({x}\right)$ be the orbit of $x$. The length of the orbit $\operatorname{Orb} \left({x}\right)$ of $x$ is the number of elements it contains, that is:
 * $\left|{\operatorname{Orb} \left({x}\right)}\right|$