Galois group of a field extension

The Galois group of a field extension $k\subseteq E$ is the group of $k$ -automorphisms of $E$ :
$\operatorname{Gal}(E / k) = \operatorname{Aut}_k(E).$

Practice this concept with exercises

Let $k\subseteq E$ be a field extension. Verify that the set of $k$ -automorphisms of $E$ is a group under composition. It is called the Galois group.

Open exercise

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