Editing Quotient group (section)

== Motivation for the name "quotient" ==
The quotient group <math>G\,/\,N</math> can be compared to [[integer division|division of integers]].  When dividing 12 by 3 one obtains the result 4 because one can regroup 12 objects into 4 subcollections of 3 objects. The quotient group is the same idea, although one ends up with a group for a final answer instead of a number because groups have more structure than an arbitrary collection of objects: in the quotient {{tmath|1= G\,/\,N }}, the group structure is used to form a natural "regrouping".  These are the cosets of <math>N</math> in {{tmath|1= G }}.  Because we started with a group and normal subgroup, the final quotient contains more information than just the number of cosets (which is what regular division yields), but instead has a group structure itself.