1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Galios theory really stuck

  1. Nov 3, 2009 #1
    E=Q(4th root of 2, i) and G is the galios group of E over Q

    I found the minimal polynomial p(x) of 4th root of 2 over Q and Q(i) to be

    I'm trying to show

    (1) the galios group H of E over Q(i) is a normal subgroup of G

    (2) If K is the galios group of Q(i) over Q show that it is isomorphic to G/H

    so I can ultimately show that G is actually D4 (the group of symmetries)

    but I'm compeltely stuck
  2. jcsd
  3. Nov 3, 2009 #2


    User Avatar
    Science Advisor

    Okay, what have you done so far? What are the roots of the polynomial [itex]x^4= 2[/itex]? What is G? What is H?

    By the way- it is 'Galois theory'. Capital G because it is a person's name and o before i.
    Last edited by a moderator: Nov 4, 2009
  4. Nov 3, 2009 #3
    I found the minimal polynomial of 4th root of 2 over Q and Q(i) to be

    and the roots are +/-w, +/-wi where w is the 4th root of 2
  5. Nov 3, 2009 #4
    Additional hint: What is the splitting field of [itex]x^4 - 2[/itex] over Q?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook