Here's the problem:
Okay, here we go ladies and gents!Given that H, K, and N are subgroups of G with H < N, and HK = HK. Prove H = N.
<--From the previous problem in the set
<-- HK = NK
<--N, K < G are groups
Thus we have that
But we know that H < N, so . Thus N = H.
Are there any assumptions or (gasp) errors that I have made in the above? Thanks!
Edit: Actually I think I can just go since and couldn't I?