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 $\operatorname{Gal} \left({K^{\operatorname{sep} } \mid K}\right)$ of its separable closure.


Definition 2

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


Also see