Let be an (irreducible) separable quartic over K and u a root of . There is

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Let ∫ be an (irreducible) separable quartic over K and u a root of ∫. There is no field properly between K and K(u) if and only if the Galois group of ∫ is either A₄ or S₄.

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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 16, 2023 03:50 AM

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Let be an (irreducible) separable quartic over K and u a root of . There is

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This is the statement of the Kleins criterion for solvability by radicals Heres a proof of the forwa...View the full answer

Algebra Graduate Texts In Mathematics 73

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