commutator length
commutator length · commutator lengths
The number of multiplicands needed, at a minimum, to express a given group element as…The number of multiplicands needed, at a minimum, to express a given group element as a product of commutators.
Meaning
2 sensesThe 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.
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
plural: commutator lengths| Singular | commutator length |
|---|---|
| Plural | commutator lengths |
regular