Galois group of a field extension
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8/11/2026, 3:23:37 PM · Nugget
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8/7/2026, 9:16:49 AM · Ancient Tree
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8/7/2026, 9:14:24 AM · Ancient Tree
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linked exercisesNoneGroup of -automorphisms
Revision 1032
8/7/2026, 9:10:06 AM · Ancient Tree
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domainGeneral algebraGalois theory
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The Galois group of a field extension $k\subseteq E$ is the [[Group|group]] of $k$-automorphisms of $E$:1
The Galois group of a [[Field extension|field extension]] $k\subseteq E$ is the [[Group|group]] of $k$[[$K$-automorphism|-automorphisms]] of $E$:2
$$\operatorname{Gal}(E / k) \cong \operatorname{Aut}_k(E)$$2
$$\operatorname{Gal}(E / k) = \operatorname{Aut}_k(E).$$Revision 285
7/7/2026, 12:42:35 PM · Ancient Tree
Concept edited
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The Galois group of a field extension $k\subseteq E$ is the group of $k$-automorphisms of $E$:1
The Galois group of a field extension $k\subseteq E$ is the [[Group|group]] of $k$-automorphisms of $E$:2
$$\operatorname{Gal}(E / k) \cong \operatorname{Aut}_k(E)$$Revision 284
7/7/2026, 12:42:04 PM · Ancient Tree
Concept created
The Galois group of a field extension $k\subseteq E$ is the group of $k$-automorphisms of $E$:
$$\operatorname{Gal}(E / k) \cong \operatorname{Aut}_k(E)$$