# Category:Stabilizers

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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.

## Pages in category "Stabilizers"

The following 17 pages are in this category, out of 17 total.

### G

### S

- Stabilizer in Group of Transformations
- Stabilizer is Normal iff Stabilizer of Each Element of Orbit
- Stabilizer is Subgroup
- Stabilizer of Cartesian Product of Group Actions
- Stabilizer of Coset Action on Set of Subgroups
- Stabilizer of Coset under Group Action on Coset Space
- Stabilizer of Element after Group Action
- Stabilizer of Element of Group Acting on Itself is Trivial
- Stabilizer of Element under Conjugacy Action is Centralizer
- Stabilizer of Polynomial
- Stabilizer of Subgroup Action is Identity
- Stabilizer of Subgroup Action on Left Coset Space
- Stabilizer of Subset Product Action on Power Set
- Stabilizers of Elements in Same Orbit are Conjugate Subgroups