a. Is |G(E/F)| multiplicative for finite towers of finite extensions, that is, is |G(E/F)| = |G(K/E)||G(E/F)| for

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a. Is |G(E/F)| multiplicative for finite towers of finite extensions, that is, is |G(E/F)| = |G(K/E)||G(E/F)| for F ≤ E ≤ K ≤ F?
Why or why not?

b. Is G(E/F)| multiplicative for finite towers of finite extensions, each of which is a splitting field over the bottom field? Why or why not?

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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. Is |G(E/F)| multiplicative for finite towers of finite extensions, that is, is |G(E/F)| = |G(K/E)||G(E/F)| for

Question:

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a This multiplicative relation is not necessarily true Example 509 and Exercise 7 show that ...View the full answer

A First Course In Abstract Algebra

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