Inmathematics, the absolute Galois group GK of a field K is the Galois groupofKsep over K, where Ksep is a separable closureofK. Alternatively it is the group of all automorphisms of the algebraic closureofK 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, Ksep is the same as an algebraic closure KalgofK. This holds e.g. for Kofcharacteristic zero, or Kafinite field.)
(For the notation, see Inverse limit.)