Answered: Let p1, p2, ..., pk ∈ N be k distinct…

Let p1, p2, ..., pk ∈ N be k distinct prime numbers. PROVE that Gal(Q(√p1,√p2, ..., √pk)/Q) isomorphism to (Z2)^k. Here (Z2)^k means the direct product, Z2 ×...×Z2, of k-copies of Z2.

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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Let p1, p2, ..., pk ∈ N be k distinct prime numbers. PROVE that Gal(Q(√p1,√p2, ..., √pk)/Q) isomorphism to (Z2)^k. Here (Z2)^k means the direct product, Z2 ×...×Z2, of k-copies of Z2.

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