Definition:Kernel of Group Action/Definition 1

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 set:

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

Sources

• 2003: David S. Dummit and Richard M. Foote: Abstract Algebra (3rd ed.) ... (previous) Chapter $1$: Introduction to Groups: $\S 1.7$: Group Actions