Definition:Effective Transformation Group

Definition

Let $G$ be a group whose identity is $e$.

Let $X$ be a set.

Let $\phi: G \times X \to X$ be a group action.

Then $G$ is an effective transformation group for $\phi$ if and only if $\phi$ is faithful.

Sources

• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Sylow Theorems: $\S 53 \gamma$