this problem is on dummit, "abstract Algebra",
Let , with . Prove the following:
(a). Z( if n is odd.
(b). Z( if n=2k.
I gave a short bit of thought before this, wondering if there was an easier, more subtle proof. I have just realised that there is. So here is a definition and a hint:
We can define the group thus: .
Now, when does the equality hold, and why is this relevant here?