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commutator length

commutator length noun: the number of multiplicands needed, at a minimum, to express a given group element as a product of commutators.

Noun

commutator length (plural commutator lengths)

  1. The number of multiplicands needed, at a minimum, to express a given group element as a product of commutators.
    • In #92;langlea,b#124;b²#61;1#92;rangle, the commutator length of aba#123;-2#125;ba is two, since it equals (aba#123;-1#125;b#123;-1#125;)(b#123;-1#125;a#123;-1#125;ba) but isn't a commutator.
  2. The supremum, over all elements of a given group's derived subgroup, of their commutator lengths.
    • The commutator length of #92;langlea,b#124;b²#61;1#92;rangle is at least two, since there's an element of commutator length two in it.

Forms of commutator length

pluralcommutator lengths

Words formed from commutator length

  • stable commutator length

Questions about commutator length

What does commutator length mean?
Commutator length means the number of multiplicands needed, at a minimum, to express a given group element as a product of commutators.
What part of speech is commutator length?
Commutator length is a noun.
What is the plural of commutator length?
The plural of commutator length is commutator lengths.

Words near commutator length in the dictionary

  1. commutatively
  2. commutativeness
  3. commutativities
  4. commutativity
  5. commutator
  6. commutator length
  7. commutator lengths
  8. commutator subgroup
  9. commutator subgroups
  10. commutatorless
  11. commutators

Source and license

Adapted from Wiktionary: commutator length (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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