Lie Algebras and Lie Groups
Abelianization is the process of transforming a given group into its abelian (or commutative) form by taking the quotient of the group by its commutator subgroup. This process allows one to simplify the structure of the group, revealing properties that are inherent to abelian groups. In the context of covering groups and the fundamental group, abelianization helps in understanding how paths in a space can be simplified into loops and how these loops can be treated as equivalent under homotopy.
congrats on reading the definition of abelianization. now let's actually learn it.