Let be a separable cubic with Galois group S 3 and roots u 1 ,u 2
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Let ∫ be a separable cubic with Galois group S3 and roots u1,u2,U3 ϵ F. Then the distinct intermediate fields of the extension of K by F are F, K(Δ), K(u1), K(u2), K(u3), K. The corresponding subgroups of the Galois group are 1 ,A3, T1, T2 , T3 and S3 where Ti = {(1),(jk) |j ≠ i ≠ k}
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We can use the fact that the Galois group of a separable polynomial of degree 3 is isomorphic to S3 ...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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