Examples in Galois Theory 3 - Polynomials of Prime Degree and Pairs of Nonreal Roots

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IntroductionIn the previous post weare convinced that the Galois group of a separable irreduciblepolynomial \(f\) can be realised as asubgroup of the symmetric group, the elements of which permute the rootsof \(f\). We worked on cubicpolynomials over a field with characteristic not equal to \(2\) an……