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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.
- commutator lengths
- plural form of commutator length
Related Terms
commutator length
Hyphenation
com·mu·ta·tor lengthPronunciation
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