Category:Group Commutators

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:

$h \circ g \circ c := g \circ h$