Definition:Commutator of Group Elements/Definition 2

Definition

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

Let $g, h \in G$.

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

$h \circ g \circ c := g \circ h$

Also see

• Equivalence of Definitions of Commutator of Group Elements

• Results about commutators of group elements can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): commutator
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): commutator