Noun
abelianization (plural abelianizations)
(mathematics) A homomorphism that transforms a group into an abelian group.
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
See above for the definition of a group's abelianization. Source: Internet
The abelianization functor is the left adjoint of the inclusion functor from the category of abelian groups to the category of groups. Source: Internet
Thus a 3-cycle like (123) must map to the same element as its inverse (321), but thus must map to the identity, as it must then have order dividing 2 and 3, so the abelianization is trivial. Source: Internet