Absolute Galois Group

In mathematics, the absolute Galois group GK of a field K is the Galois group of Ksep over K, where Ksep 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, Ksep is the same as an algebraic closure Kalg 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

Famous quotes containing the words absolute and/or group:

    ... the absolute freedom of woman will be the dawn of the day of man’s regeneration. In raising her he will elevate himself.
    Tennessee Claflin (1846–1923)

    The trouble with tea is that originally it was quite a good drink. So a group of the most eminent British scientists put their heads together, and made complicated biological experiments to find a way of spoiling it. To the eternal glory of British science their labour bore fruit.
    George Mikes (b. 1912)