Answered: for all nEN there are infinitely many…

for all nEN there are infinitely many prime numbers p=^ (modu) Prove that for each finite abelian group G there is a number field K such that G = Gal (K/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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Dirichlet's Theorem says that for all natural numbers n there are infinitely many prime numbers p ≡ 1 (mod n). Prove that for each abelian group G there is a number field K such that G = Gal(K/Q). Q is the field of rational numbers.

for all nEN there are
infinitely many prime numbers p=^ (modu)
Prove that for each finite abelian group G there is a number field K
such that G = Gal (K/Q).

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