Prove that is not isomorphic to a proper subgroup of itself.
So, far i have:
Let not in
Since is bijective for some
I know there's a contradiction here, but I can't see it
However, the result you used is true, but needs to be proven.
Notice that for , . So the result now just needs to be shown for the denominators.
as the kernel is trivial.
Thus, as required.
Or something along those lines...