Phrase guide

commutator length

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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Pronunciation

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1

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Examples

  • 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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

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

Definition source: English Wiktionary via Wiktextract

Examples

  • 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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.