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
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 3.3$: Group actions and coset decompositions: Examples of group actions: $\text{(iii)}$