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At a total loss with these Galois groups.

  1. Oct 31, 2009 #1
    I've been asked to match some galois groups with structures like:

    Z_2, Z_3, Z_2 X Z_2 ...etc.

    And I'm very much lost. I know the galois group for a field extension L:K is the set of isomorphism that fix F. These form a group with function composition.

    OK. But how do I find these isomorphism. The book has one example and they gloss over that step... my instructor only did it for a cases where it was really obvious that it was conjugation. So, I'm feeling lost.


    One of the problems is a little like this:

    [tex]Q(\sqrt{3}, \sqrt{2}): Q[/tex]

    [tex]Q(\sqrt{3}, \sqrt{2})= Q(\sqrt{3}+ \sqrt{2})[/tex]

    So the minimal polynomial is

    [tex]x^2 = 5 + 2\sqrt{6}[/tex]

    [tex]x^4 -10x^2 + 1[/tex]

    The degree is 4.

    Here the intermediate fields are [tex]Q(\sqrt{3}), Q (\sqrt{2})[/tex] ... but are there more?

    in any case how do I find the elements in the Galois group ...

    The identity... and...?
     
    Last edited: Oct 31, 2009
  2. jcsd
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