markus endres on 27 Feb 2003 15:06:37 +0100

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assume L|K|Q is a tower of fields (Q the rationals). 
L|K a galois extension.

then nfgaloisconj(L) determines the automorphisms from L over Q, hence
the galois group gal(L|Q) contains these automorphisms defined over Q.

but now, I want to compute the galois group gal(L|K).(ok, this is easy.
I look at the automorphisms of gal(L|Q) which fixes K pointwise). 

now, I have gal(L|K) with automorphisms defined over Q, but I need these
automorphisms defined over K. 

How can I do this?

thx in advance