So letLet . Prove that for any fixed integer k > 1 the map from G to itself defined by is a surjective homomorphism but is not injective.

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Proving the homomorphism is trivial. It's the surjection part that's getting to me. (I haven't tackled the injection yet. Please leave that out of the replies for now.) What I am looking at is the following...I want to show that there is at least one pair of x, y in G such that is true when x is not equal to y. My other question about this is do we need to find an x, y for each k? For example, is only true for even k.

I'm just not wrapping this one around in my head today.

Thanks!

-Dan