Definition:Absolute Galois Group

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Definition

Let $K$ be a field.


Definition 1

The absolute Galois group of $K$ is the Galois group $\Gal {K^{\operatorname{sep} } \mid K}$ of its separable closure.


Definition 2

The absolute Galois group of $K$ is the automorphism group $\Aut {\overline K \mid K}$ of its algebraic closure.


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