Definition:Trivial Group Action

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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

  • Results about the trivial group action can be found here.


Sources