Splitting fields and Symmetric groups.

From: jamesdickerson00@xxxxxxxxxxx
Date: 2 Jun 2005 11:41:10 -0700

This is a puzzling problem. It might even be easy but I'm not having
any success.

Suppose that E is Galois over F and Gal(E/F) is isomorphic to a
transitive subgroup of the symmetric group S_n. Show that E is a
splitting field over F for some irreducible polynomial f in F[x]with
deg(f)=n.

.

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