Let F be a field and let be a primitive nth root of unity in F,

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Let F be a field and let ζ be a primitive nth root of unity in F, where the characteristic of F is either 0 or does not divide n.
a. Show that F(ζ) is a normal extension of F.
b. Show that G(F(ζ/F) is abelian.

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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Jan 16, 2023 02:50 AM

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Let F be a field and let be a primitive nth root of unity in F,

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a Exercise 17 of Section 51 shows that x n 1 has no zero...View the full answer

A First Course In Abstract Algebra

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