Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to determine galois group?

  1. Feb 19, 2009 #1
    I have trouble in determining Galois group.
    Can anyone help me with the following question:

    how to determine the Galois group of (x^2-2)(x^2-3)(x^2-5), determine all the subfields of the splitting field of this polynomial?

    how to determine the elements of the galois group of x^p-2 for p is prime.

    Thanks a lot!
  2. jcsd
  3. Feb 20, 2009 #2


    User Avatar
    Science Advisor

    The set of solutions of xp= a are of the form [itex]|a|^{1/p}\omega^i[/itex] with i ranging from 0 to p-1, where [itex]\omega[/itex] is the "principal pth root of unity". The Galois group is the permutation group of that set: the permutation group on p objects.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook