# Category:Conjugacy Action

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This category contains results about **Conjugacy Action**.

Definitions specific to this category can be found in Definitions/Conjugacy Action.

Let $\struct {G, \circ}$ be a group.

The **(left) conjugacy action** of $G$ is the left group action $* : G \times G \to G$ defined as:

- $\forall g, x \in G: g * x = g \circ x \circ g^{-1}$

The **right conjugacy action** of $G$ is the right group action $* : G \times G \to G$ defined as:

- $\forall x, g \in G: x * g = g^{-1} \circ x \circ g$

## Subcategories

This category has only the following subcategory.

## Pages in category "Conjugacy Action"

The following 12 pages are in this category, out of 12 total.

### C

- Center of Group is Kernel of Conjugacy Action
- Conjugacy Action is Group Action
- Conjugacy Action is not Transitive
- Conjugacy Action on Abelian Group is Trivial
- Conjugacy Action on Group Elements is Group Action
- Conjugacy Action on Identity
- Conjugacy Action on Subgroups is Group Action
- Conjugacy Action on Subsets is Group Action