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  1. A

    Onto vs into

    Same, all the books I have seen in Algebra use onto when the function is surjective, otherwise they say into.
  2. A

    Galois Extension of Q isomorphic to Z/3Z

    When I wrote the above I was thinking of x as a natural number or integer, in which case it should work as an example of a Galois group isomorphic to Z/3Z. But as for a complete generalization, I do not know of how to give it.
  3. A

    Galois Extension of Q isomorphic to Z/3Z

    Let d=cubic root of some number x s.t. d is not in Q. Then [Q(d):Q]=3 => o(Gal(Q(d)/Q))=3 and only group of order 3 is Z/3Z so you have your desired group.
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