# Category:Definitions/Conjugacy

This category contains definitions related to Conjugacy in the context of Group Theory.
Related results can be found in Category:Conjugacy.

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

### Definition 1

The conjugacy relation $\sim$ is defined on $G$ as:

$\forall \tuple {x, y} \in G \times G: x \sim y \iff \exists a \in G: a \circ x = y \circ a$

### Definition 2

The conjugacy relation $\sim$ is defined on $G$ as:

$\forall \tuple {x, y} \in G \times G: x \sim y \iff \exists a \in G: a \circ x \circ a^{-1} = y$

## Subcategories

This category has only the following subcategory.

## Pages in category "Definitions/Conjugacy"

The following 9 pages are in this category, out of 9 total.