Noun
commutator subgroup (plural commutator subgroups)
The subgroup of a specified group generated by the larger group's commutators.
If X is path-connected, then this homomorphism is surjective and its kernel is the commutator subgroup of π 1 (X, x 0 ), and H 1 (X) is therefore isomorphic to the abelianization of π 1 (X, x 0 ). Source: Internet
This shows that the commutator subgroup can be viewed as a functor on the category of groups, some implications of which are explored below. Source: Internet