commutator length

English - English

Definition of commutator length in English English dictionary

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

In \langle a,b|b^2=1\rangle, the commutator length of aba^{-2}ba is two, since it equals (aba^{-1}b^{-1})(b^{-1}a^{-1}ba) but isn't a commutator.

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

The commutator length of \langle a,b|b^2=1\rangle is at least two, since there's an element of commutator length two in it.

Related Terms

commutator lengths

plural form of commutator length

Hyphenation

com·mu·ta·tor length