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Math Help - quesions about radical and cyclotomic extensions

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    quesions about radical and cyclotomic extensions

    (1) Give a example of a polynomials such that its splitting field is contained in a radical extension over but is not radical over
    (2)Let and .
    Find and all intermediate fields between and.
    (3)Which roots of unity are contained in ,where is a square free integer?
    (4)Let . what does "Solve for by radicals" mean?

    Thanks for any help.
    Last edited by laipou; April 21st 2010 at 01:58 AM.
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