(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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. Relevant 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.

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# Homework Help: Conjugate Subgroups

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