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commutator length

noun

Definitions

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

    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…

    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.

The neighborhood

Vish — recursive loop

No curated loop yet for commutator length. Loops are being traced one word at a time while the ingestion pipeline matures.

sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA