Ok, so there is this problem that quite confuses me because the example seems too easy (at least thats what I think):
Find an example of a group homomorphism $\Phi: S_3 \rightarrow S_4$ that is injective.
I think the example is just $\Phi(\sigma)=\sigma$, this is the only example I can think about but I am not sure if it is correct. Can anyone tell me if this example is valid? If not what other examples could there be?