Let f(x) F[x] be a polynomial such that every irreducible factor of f(x) is a separable

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Let f(x) ∈ F[x] be a polynomial such that every irreducible factor of f(x) is a separable polynomial over F. Show that the group of f(x) over F can be viewed in a natural way as a group of permutations of the zeros of f(x) in 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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Let f(x) F[x] be a polynomial such that every irreducible factor of f(x) is a separable

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Let K be the splitting field of fx over F Because each GKF carries a zero of fx ...View the full answer

A First Course In Abstract Algebra

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