# Definition:Absolute Galois Group

## 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.