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??
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What sort of automorphisms do you mean? As a vector space or as an algebra? – Tobias Kildetoft Jan 31 '17 at 08:48
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automorphism as field. – log log Jan 31 '17 at 08:52
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and $\forall \sigma \in G \ ,\ \sigma | \mathbb{Q} = {id}{\mathbb{Q}} $ – log log Jan 31 '17 at 08:54
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That last part follows from being an automorphism of fields. – Tobias Kildetoft Jan 31 '17 at 08:58
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I don't understand $K \subset \mathbb{Q}$. Please prove it. – log log Jan 31 '17 at 09:02
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I meant the last part you wrote in the comments. – Tobias Kildetoft Jan 31 '17 at 09:03