Commutator Subgroup

The commutator subgroup, also called the derived subgroup, of a group in abstract algebra is the subgroup generated by all of the group's commutators. It is important because it is the smallest normal subgroup whose quotient group is abelian: for a normal subgroup N of a group G, the quotient G/N is abelian exactly when N contains the commutator subgroup, so in this sense the commutator subgroup measures how far a group is from being abelian, since the larger it is, the further the group is from commuting. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/