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**1. Homework Statement**

How would I go about proving that if K = gHg

^{-1}, for some g [itex]\in[/itex]G, where K and H are both subgroups of G with a prime number of elements, then K = H?

**2. Homework Equations**

I've tried to prove it by saying that if K = gHg

^{-1}then Kg = gH, and since H = gHg

^{-1}, then Hg = gH also, so Hg = Kg, and hence H = K. I don't think that this proof is valid, unfortunately. And I've just realised that H does not necessarily equal gHg

^{-1}unless g is in the normaliser of H. :(

**3. The Attempt at a Solution**

This is actually something which I am attempting to prove in order to prove something else, so I'm not even sure if what I'm trying to prove holds at all. I just need K = H for my proof to work.