Fill in the blank. A Galois group of E over F is a group of automorphisms of E that _______________ F elementwise (that is, f: Aut(E), such that f(a) = a for all a in F).

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Fill in the blank. A Galois group of E over F is a group of automorphisms of E that _______________ F elementwise (that is, f: Aut(E), such that f(a) = a for all a in F).