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The question is:

Let L / K be a finite (not necessarily Galois) extension of algebraic number fields and N / K the normal closure of L / K. Show that a prime ideal p of K is totally split in L if and only if it is totally split in N. Hint: Use the double coset decomposition H\G/GP, where G = G(N/K), H = G(N/L) and GP , is the decomposition group of a prime ideal P over p.

My question is how to use this hint to solve this problem; please give me some advice.

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This is dealt with in my answer here. Voting to close. –  Arturo Magidin May 17 '11 at 16:32
    
.......thank you –  dust May 17 '11 at 16:34
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And in my answer here: math.stackexchange.com/questions/33573/… –  Alex B. May 17 '11 at 16:36
    
@Alex:Thanks but I can not see your answer there...it seems that there is something wrong with the internet... –  dust May 17 '11 at 17:25
    
I can; the link works perfectly fine. Maybe something wrong on your end. –  Arturo Magidin May 17 '11 at 18:39

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