Definition:Galois Group

Disambiguation

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Galois Group may refer to:

Galois Group of Field Extension

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:

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

Galois Group of Polynomial

Let $P$ be a polynomial.

The Galois group of $P$ is the symmetry group of the roots of $P$.

Source of Name

This entry was named for Évariste Galois.