Let f(x)∈F[x] be separable of degree n and let K be the splitting field of f(x)....

Let f(x)∈F[x] be separable of degree n and let K be the splitting field of f(x). Show that the order of Gal(K/F) divides n!.

Expert Solution

Colby Messinger answered 1 year ago

Let f be an irreducible polynomial of degree n over K, and let Σ be the...

Let f be an irreducible polynomial of degree n over K, and let Σ be the splitting field for f over K. Show that [Σ : K] divides n!.

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Let f(x)∈F[x] be separable of degree n and let K be the splitting field of f(x)....

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