The set of automorphisms of a field $K$ (i.e. the bijective field homomorphisms from $K$ to $K$), denoted ${\rm Aut}(K)$, forms a group under composition of maps.

Let $K$ be a field extension of a field $F$. The **group of automorphisms of $K/F$**, also called the **group of $F$-automorphisms of $K$**, is given by the set:

${\rm Aut}_F(K):=\{\sigma\in{\rm Aut}(K)\mid \sigma(x)=x,\; {\rm all}\;x\in F\}$ under

composition of maps

...and is a subgroup of ${\rm Aut}(K)$.

Which of the following are true?

Select **ALL** that apply.