Galois group of a polynomial
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7/7/2026, 12:46:30 PM · Ancient Tree
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The Galois group of a [[Polynomial|polynomial]] $P$ of $K[X]$ is the [[Galois group of a field extension|Galois group]] of a [[Splitting field|splitting field]] $k\subseteq E$ of $P$:1
The Galois group of a [[Polynomial|polynomial]] $P$ of $K[X]$ is the [[Galois group of a field extension|Galois group]] of a [[Splitting field|splitting field]] $K\subseteq E$ of $P$:2
$$\operatorname{Gal}_K(P)=\operatorname{Gal}(E/K)$$Revision 288
7/7/2026, 12:46:17 PM · Ancient Tree
Concept created
The Galois group of a [[Polynomial|polynomial]] $P$ of $K[X]$ is the [[Galois group of a field extension|Galois group]] of a [[Splitting field|splitting field]] $k\subseteq E$ of $P$:
$$\operatorname{Gal}_K(P)=\operatorname{Gal}(E/K)$$