Let F be normal over K and E an intermediate field. Then E is normal over K
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Let F be normal over K and E an intermediate field. Then E is normal over K if and only if E is stable [see Exercise 17]. Furthermore AutKF/E' ≅ AutKE.
Data from exercise 17
If an intermediate field E is normal over K, then E is stable (relative to F and K).
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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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