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 well-defined up to inner automorphism. 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.)
(For the notation, see Inverse limit.)