Definition:Kernel of Group Action

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Definition

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

Let $X$ be a set.

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


Definition 1

The kernel of the group action is the set:

$G_0 = \set {g \in G: \forall x \in X: g * x = x}$


Definition 2

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


Also see