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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](http://math.stackexchange.com/questions/39434/splitting-of-prime-ideals-in-algebraic-extensions/39651#39651). Voting to close.2011-05-17
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    And in my answer here: http://math.stackexchange.com/questions/33573/ramification-in-a-tower-of-extensions/33579#335792011-05-17
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    @Alex:Thanks but I can not see your answer there...it seems that there is something wrong with the internet...2011-05-17
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    I can; the link works perfectly fine. Maybe something wrong on your end.2011-05-17

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