[GAP Forum] Galois Group question
Igor Schein
igor at txc.com
Mon May 15 19:19:15 BST 2006
Dear Gap Forum,
Given a small group G of order 2^n, I would like to know whether or not
there exists a polynomial P in x^4 whose Galois group is G. Let me
illustrate:
gap> IdGroup(TransitiveGroup(8,GaloisType(x^8+3*x^4+1)));
[ 8, 3 ]
So the answer is yes for small group [8,3], P: x -> x^2+3*x+1
However, if I consider small group [8,4], such P clearly doesn't
exist, so the answer is no.
So my question is how I can answer this question using GAP commands
and intrinsic properties of groups. Specifically, I need to know the
answer for [64,64] and [64,122].
Thanks in advance and please forgive any (unintentional) ambiguity
and/or terminology misuse.
Igor
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