Answered: Given that the automorphism group of…

Given that the automorphism group of Q(√2, √5, √7) is isomorphicto Z2 ⊕ Z2 ⊕ Z2, determine the number of subfields of Q(√2,√5, √7) that have degree 4 over Q.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 38E

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Question

Given that the automorphism group of Q(√2, √5, √7) is isomorphic
to Z₂ ⊕ Z₂ ⊕ Z₂, determine the number of subfields of Q(√2,
√5, √7) that have degree 4 over Q.

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