Web:foorP De nition 2.3 For elds F Ede ne aut(EjF) to be the set of all automorphisms ˙of Ewhich x F, i.e., ˙(a) = afor all a2F. Proposition 2.4 aut(EjF) is a group. Furthermore, if F E Kare elds, then aut(KjE) is a subgroup of aut(KjF). Proof: If ˙;˝2aut(EjF), then clearly ˙ ˝is an automorphism of E. Given a2Fwe have

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