Definition:Kernel of Group Action/Definition 2

Definition

Let $G$ be a group with identity $e$.

Let $X$ be a set.

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

The kernel of the group action is the kernel of its permutation representation.

Sources

• 2008: I. Martin Isaacs: Finite Group Theory ... (previous) Chapter $1$: Sylow Theory: $\S 1A$