commutator length

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

In , the commutator length of is two, since it equals but isnt a commutator.

b) The supremum, over all elements of a given groups derived subgroup, of their commutator lengths.

The commutator length of is at least two, since theres an element of commutator length two in it.


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