Definition:Commutator/Group
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Definition
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:
- $h \circ g \circ c := g \circ h$
Also see
- Results about commutators of group elements can be found here.