Definition:Trivial Group Action

Definition
Let $G$ be a group.

Let $S$ be a set.

Let $*: G \times S \to S$ be the group action defined as:
 * $\forall \tuple {g, s} \in G \times S: g * s = s$

Then $*$ is the trivial group action of $G$ on $S$.

Also see

 * Trivial Group Action is Group Action