Category:Galois Groups of Field Extensions

This category contains results about Galois Groups of Field Extensions.
Definitions specific to this category can be found in Definitions/Galois Groups of Field Extensions.

Let $L / K$ be a field extension.

The Galois group of $L / K$ is the subgroup of the automorphism group of $L$ consisting of field automorphisms that fix $K$ point-wise:

$\Gal {L / K} = \set {\sigma \in \Aut L: \forall k \in K: \map \sigma k = k}$