A Polynomial Time Nilpotence Test for Galois Groups and Related Results
نویسندگان
چکیده
We give a deterministic polynomial-time algorithm to check whether the Galois group Gal (f) of an input polynomial f(X) ∈ Q[X] is nilpotent: the running time is polynomial in size (f). Also, we generalize the Landau-Miller solvability test to an algorithm that tests if Gal (f) is in Γd: this algorithm runs in time polynomial in size (f) and n d and, moreover, if Gal (f) ∈ Γd it computes all the prime factors of #Gal (f).
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