nLab
free action

Definition

An action

$$\rho :G\times X\to X$$\rho : G \times X \to X

of a group $G$ on a set $X$ is free if for every $x\in X$ and every $g\in G$, the equation $gx=x$ implies $g=1_G$.

Related concepts

• homogeneous space
• transitive action
• torsor