Determine the Galois groups of the following polynomials over the fields indicated (a) x 4 5 over Q over (b) (x 3 2)(x 2 3)(x 2 5)(x 2 7) over Q (c) x 3 x 1 over Q over (d) x 3 10 over Q over (e) x 4 3x 3 3x 2 over Q (f) x 5 6x 3 over Q (g) x 3 2 over Q (h) (x 3 2)(x 2 5) over Q (i) x 4 4x 2 5 over...

a For the polynomial x4 5 over Q Galois group over Q S4 the symmetric group on 4 elements Galois gro ...

Determine the Galois groups of the following polynomials over the fields indicated: (a) x 4 - 5

Question:

Determine the Galois groups of the following polynomials over the fields indicated:

(a) x⁴ - 5 over Q; over

(b) (x³ - 2)(x² - 3)(x² - 5)(x² - 7) over Q.

(d) x³ - 10 over Q; over

(e) x⁴ + 3x³ + 3x - 2 over Q.

(f) x⁵- 6x + 3 over Q.

(g) x³ - 2 over Q.

(h) (x³ - 2)(x² - 5) over Q.

(i) x⁴ - 4x² + 5 over Q.

(j) x⁴ + 2x² + x + 3 over Q.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 20, 2023 02:58 AM

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Determine the Galois groups of the following polynomials over the fields indicated: (a) x 4 - 5

Question:

Q(√5); over Q(√5i).

Step by Step Answer:

a For the polynomial x4 5 over Q Galois group over Q S4 the symmetric group on 4 elements Galois gro...View the full answer

Algebra Graduate Texts In Mathematics 73

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