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Math Help - Galois group of the algebraic closure of the rationals

  1. #1
    MHF Contributor Bruno J.'s Avatar
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    Galois group of the algebraic closure of the rationals

    An absolutely fascinating object since we know so little about it. I'd love to learn more but I haven't been able to find much information.

    If anyone can shed a tiny bit of light about this for me, please do so!
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  2. #2
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    Quote Originally Posted by Bruno J. View Post
    An absolutely fascinating object since we know so little about it. I'd love to learn more but I haven't been able to find much information.

    If anyone can shed a tiny bit of light about this for me, please do so!
    I do not know anything about it myself but I would imagine you need to know infinite Galois theory. That is when K/F is a Galois extension but [K:F] = \infty. The standard results to the study of subgroups \text{Gal}(K/F) no longer apply, only very specific subgroups are now considered. Have you ever seen this kind of stuff before?
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