We need only show that the set of automorphisms of E that fix F elementwise is a subgroup of the group of all automorphisms of E. Let σ and τ be two automorphisms of...We need only show that the set of automorphisms of E that fix F elementwise is a subgroup of the group of all automorphisms of E. Let σ and τ be two automorphisms of E such that σ(α)=α and τ(α)=α for all α∈F. Then στ(α)=σ(α)=α and σ−1(α)=α. Since the identity fixes every element of E, the set of automorphisms o…