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 _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
