(i) A portion of the table of automorphisms of E that fix Q has been filled in below. Com-plete the rest of the table.-7V2V3V30 0 02 0 0, -0,(i) Are the intermediate fields Q(v2) and Q(V3) conjugate fields? Justify your reasoning.(k) Use the Fundamental Theorem of Galois Theory (Theorem 23.22) to show the cor-respondence between cach subgroup of G(E/Q) and its intermediate field of E overQ.

Note that values of thetas are not given, hence the table can not be completed fully as we require…

Answered: (i) A portion of the table of…

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 6TFE

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(i) A portion of the table of automorphisms of E that fix Q has been filled in below. Com- plete the rest of the table. -7 V3 (1) Are the intermediate fields Q(V2) and Q(V3) conjugate fields? Justify your reasoning.