quotient groups

[DanGrayson]

Wouldn't it make sense for quotient groups to be defined in the way strictly dual to the way subgroups are defined? Here are the two definitions:

Then the connection with normal subgroups would be drawn.

And quotient groups could have their own chapter, too, since subgroups do.

[DanGrayson]

In other words, I propose changing "set of surjections" to "type of quotient groups".

And also starting more gently, by saying that a quotient group of G is an epimorphism from G to a group.

[DanGrayson]

By the way, it seems to be left unproved that the set of surjections from G is a set.