Describe a group homomorphism from to .
is the group of units under multiplication
is the set of permutations on 4 elements.
The hint for the exercise said to use Cayley's Theorem.
Well, what is Cayley's theorem?
The hint is telling you, basically, to work through the proof of Cayley's theorem using an example. There are a number of different homomorphisms from to , but the point of this question is not to conjure up these, but to find a specific one using this theorem.
So, do you have any problems understanding the theorem? It basically says you can find a `copy' of in .