# Category:Group Commutators

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This category contains results about **Group Commutators**.

Definitions specific to this category can be found in Definitions/Group Commutators.

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

Let $g, h \in G$.

### Definition 1

The **commutator** of $g$ and $h$ is the element of $G$ defined and denoted:

- $\sqbrk {g, h} := g^{-1} \circ h^{-1} \circ g \circ h$

### Definition 2

The **commutator** of $g$ and $h$ is the element $c$ of $G$ with the property:

- $h \circ g \circ c := g \circ h$

## Subcategories

This category has only the following subcategory.

## Pages in category "Group Commutators"

The following 8 pages are in this category, out of 8 total.