TITLE: Who named "Quotient groups"?
QUESTION [30 upvotes]: Who decided to call quotient groups quotient groups, and why did they choose that name? A lot of identities such as $$\frac{G/A}{B/A}\cong \frac{G}{B}$$ suggest that whoever invented the notation understood these things a lot better than I do...
Edit: I'm also interested in the notation; I was assuming that the notation and terminology went together, but perhaps that is not the case.

REPLY [2 votes]: If the group $G$ has $24$ members and a normal subgroup $H$ has $6$ members, then $G/H$ has $24/6$ members and $24/6$ is clearly a quotient.  Division is an operation on numbers defined initially by thinking about finite sets: split a set of $24$ members into parts of size $6$; then how many such parts are there?  Clearly that is a quotient, in the sense of a number that results from division, and clearly that's how quotient groups are formed: a quotient group is a group of cosets.
(This is "quotition division" as opposed to "partition division".)