nLab group commutator

Definition

For $g,h \in G$ a pair of elements of a group, their group commutator is the element

$$[g,h] \coloneqq g^{-1} \cdot h^{-1} \cdot g \cdot h \,.$$

This definition clearly generalizes to invertible semigroups.

Related concepts

• commutator subgroup

• commutator

• Lie bracket

• Samelson product