commutator length

noun

The number of multiplicands needed, at a minimum, to express a given group element as a product of commutators.

意味（1）

The number of multiplicands needed, at a minimum, to express a given group element as a product of commutators.

In ⟨a,b|b²=1⟩, the commutator length of aba⁻²ba is two, since it equals (aba⁻¹b⁻¹)(b⁻¹a⁻¹ba) but isn't a commutator.

意味（2）

The supremum, over all elements of a given group's derived subgroup, of their commutator lengths.