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.

Given: The automorphism group of Q2, 5, 7 is isomorphic to Z2⊕Z2⊕Z2.To find: The number of subfields…

Answered: Given that the automorphism group of…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 31E

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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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