Some General Results
- Every profinite group occurs as a Galois group of some Galois extension, however not every profinite group occurs as an absolute Galois group. For example, the Artin–Schreier theorem asserts that the only finite absolute Galois groups are the trivial one and the cyclic group of order 2.
- Every projective profinite group can be realized as an absolute Galois group of a Pseudo algebraically closed field. This result is due to Alexander Lubotzky and Lou van den Dries.
Read more about this topic: Absolute Galois Group
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