Let $G={\rm \mathit Aut} _\mathbb{Q} (\mathbb{C})$ be the automorphism group.
$K \subset \mathbb{C}$ is defined as $K =\ \bigr\{ \alpha \in \mathbb{C} \ |\ \sigma(\alpha) = \alpha \ ( \forall \sigma \in G)\bigl\}$ .
Then $K= \mathbb{Q} \ $ is true??
Is the next claim about automorphism group ${\rm \mathit Aut} _\mathbb{Q} (\mathbb{C})$ correct?
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$\begingroup$
group-theory
field-theory
galois-theory
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0What sort of automorphisms do you mean? As a vector space or as an algebra? – 2017-01-31
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0automorphism as field. – 2017-01-31
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0and $\forall \sigma \in G \ ,\ \sigma | _\mathbb{Q} = {id}_{\mathbb{Q}} $ – 2017-01-31
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0That last part follows from being an automorphism of fields. – 2017-01-31
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0I don't understand $K \subset \mathbb{Q}$. Please prove it. – 2017-01-31
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0I meant the last part you wrote in the comments. – 2017-01-31