# Category:Stabilizers

This category contains results about Stabilizers.

Let $G$ be a group.

Let $X$ be a set.

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

For each $x \in X$, the stabilizer of $x$ by $G$ is defined as:

$\Stab x := \set {g \in G: g * x = x}$

where $*$ denotes the group action.

## Subcategories

This category has only the following subcategory.