Let f(x) = Q[x] be a irreducible polynomialof prime degree p. If f(x) has exactly twonon-real roots then the Galois groupG of f(x) over Q is isomorphic to Sp.

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 8E: Let be an irreducible polynomial over a field . Prove that is irreducible over for all nonzero ...

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Let f(x) = Q[x] be a irr of prime degree p. If fr non-real roots then th