Your examples of type f:= x^6+ax+b have galois group (use maple) S3 wr S3 of order 72.
Solvable 6-ic polynomials are treated by Tom Hagedorn
in J.Alg (2000) 233 pp 704-757.
Lesser degree polynomials are treated in the book by Dummit & Foote.
John
_______________________________________________
Forum mailing list
Forum@mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum
