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absolute Galois group (Definition)

Let $ k$ be a field. The absolute Galois group $ G_k$ of $ k$ is the Galois group $ \operatorname{Gal}(k^{\operatorname{sep}}/k)$ of the field extension $ k^{\operatorname{sep}}/k$, where $ k^{\operatorname{sep}}$ is the separable closure of $ k$.



"absolute Galois group" is owned by djao. [ full author list (2) | owner history (1) ]
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Cross-references: separable closure, field extension, Galois group, field
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This is version 3 of absolute Galois group, born on 2002-01-21, modified 2004-03-14.
Object id is 1515, canonical name is AbsoluteGaloisGroup.
Accessed 3855 times total.

Classification:
AMS MSC: 12F10 (Field theory and polynomials :: Field extensions :: Separable extensions, Galois theory)
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