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Short yes/no question.

  1. Dec 30, 2009 #1
    Given a finite group G is G isomorphic to the Galois group of some polynomial in Q? Having done a course on Galois theory I think I just missed this and I feel like I ought to know the answer. Did I just sleep through that part of class?

    :/
     
  2. jcsd
  3. Dec 31, 2009 #2

    HallsofIvy

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    That's not a question. Given that a finite group G is isomorphic to the Galois group of some polynomial, what? What conclusion are you to make?
     
  4. Dec 31, 2009 #3
    I think what the question is asking is the following. If you are given some finite group, is it isomorphic to the Galois group of some polynomial in Q?
     
  5. Dec 31, 2009 #4
    I'm asking if for every finite group is there at least one polynomial in Q that has that group as its Galois group.

    That is we did a lot of "give a polynomial find the Galois group." can you do always the reverse?

    maybe this is obvious or something...
     
  6. Dec 31, 2009 #5
    Yes. This is just the question.
     
  7. Dec 31, 2009 #6

    Dick

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    That's the Inverse Galois Problem. You can search online for info. I don't think the answer is completely known.
     
  8. Dec 31, 2009 #7
    Thanks! It looks pretty cool.
     
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