What is different between $G/N$ and $GN/N$?
($G$ denotes a group, and N does a normal subgroup of G)
If you look at the element of each group above,
I think $G/N$ contains element of form $gN$, where $g$ is an element of G but not in $N$.
and $GN/N$ contains element of form $gnN$ which is equivalent to $gN$,
because $n$ is an element of $N$.
Then it looks like they indicate same group.
Is there anything wrong with my reasoning?
If so, could you point out and fix it?
$\endgroup$ 3 Reset to default
