Answered: Given that the automorphism group of…

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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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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