Question
Let $E$ be an extension field of the field $F$. Show that the automorphism group of $E$ fixing $F$ is indeed a group. (This exercise is referred to in this chapter.)
Step 1
First, we need to show that the set of automorphisms of $E$ fixing $F$ is non-empty. The identity automorphism, which maps every element of $E$ to itself, is an automorphism that fixes $F$. So, the set is non-empty. Show more…
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In each of the following, show that $H$ is a subgroup of $G$. $G=\langle\mathscr{F}(\mathbb{R}),+\rangle, H=\{f \in \mathscr{F}(\mathbb{R}): f(-x)=-f(x)\}$
SUBGROUPS
B
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