What is a commutator subgroup?

A commutator subgroup is the subgroup of a G group supported by the commutators of the elements. It is the smallest subgroup of G, and it can range from a certain subgroup to the whole group.

The commutator subgroup, also known as a derived subgroup, is a concept found in abstract algebra. The small size of the commutator subgroup makes it an important part of the abelian group, otherwise known as the commutative group. For example, the group G/N is only abelian if N includes the commutator subgroup. The commutator subgroup also measures the abelian nature of a group. A large commutator subgroup means the group is less abelian. Not every element in a commutator subgroup is considered a commutator.