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.
Also see
- Results about absolute Galois groups can be found here.