- #1

- 348

- 0

## Main Question or Discussion Point

I know the definition of the Abelianization and the most direct implications of this new group, but what I don't understand are some of the broader implications. For instance, what can we say about the number of generators of the abelianization of a group with respect to the number of generators of that group? Also, one quick question: is it true that the abelianization of the direct product of groups is the direct product of the abelianization of the components (the direct product is finite)?