A finite normal extension K of a field F is abelian over F if G(K/F) is an

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A finite normal extension K of a field F is abelian over F if G(K/F) is an abelian group. Show that if K is abelian over F and p is a normal extension of F, where F ≤ E ≤ K, then K is abelian over E and E is abelian over F.

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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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A finite normal extension K of a field F is abelian over F if G(K/F) is an

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Because FKE GKF and GKF is abelian we see that GKE is abel...View the full answer

A First Course In Abstract Algebra

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