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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
    x^4-2

    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

    HallsofIvy

    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
    x^4-2

    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?

    Petek
     
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