= Automorphism of a field extension
{title2=$\sigma\in\operatorname{Aut}_F(K)$}
= Galois automorphism
{c}
{synonym}
An automorphism of a <field extension> $K/F$ is a <field automorphism> $\sigma:K\to K$ fixing every element of $F$. Such maps form the <field automorphism group> $\operatorname{Aut}_F(K)$ under composition. For a <Finite Galois extension> this is the <Galois group> $\operatorname{Gal}(K/F)$. Specifying the fixed base <field> distinguishes these maps from arbitrary <field automorphisms> of $K$.
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