http://www.math.uwaterloo.ca/~karigian/talks/CUMC-2010.pdf
In this pdf it says that if you have a $S^{n-1}$ that admits a group structure, then you can get normed divison algebra.
How do you prove this? As I need to have a result like this as I'm trying to show there are only four Hopf maps. I'm trying to find an easy proof that there are only four Hopf maps, the easiest way I see is to prove that there are only four H-spaces that are spheres.
Anyone got any ideas how you prove the above.