In mathematics, the **absolute Galois group** *G _{K}* of a field

*K*is the Galois group of

*K*sep over

*K*, where

*K*sep is a separable closure of

*K*. Alternatively it is the group of all automorphisms of the algebraic closure of

*K*that fix

*K*. The absolute Galois group is unique up to isomorphism. It is a profinite group.

(When *K* is a perfect field, *K*sep is the same as an algebraic closure *K*alg of *K*. This holds e.g. for *K* of characteristic zero, or *K* a finite field.)

Read more about Absolute Galois Group: Examples, Problems, Some General Results

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