Galois Group - Properties

Properties

The significance of an extension being Galois is that it obeys the fundamental theorem of Galois theory: the closed (with respect to the Krull topology below) subgroups of the Galois group correspond to the intermediate fields of the field extension.

If E/F is a Galois extension, then Gal(E/F) can be given a topology, called the Krull topology, that makes it into a profinite group.

Read more about this topic:  Galois Group

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