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.
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 .