Galois group

The Galois groupMathworldPlanetmath Gal(K/F) of a field extension K/F is the group of all field automorphisms σ:KK of K which fix F (i.e., σ(x)=x for all xF). The group operationMathworldPlanetmath is given by composition: for two automorphismsPlanetmathPlanetmathPlanetmathPlanetmath σ1,σ2Gal(K/F), given by σ1:KK and σ2:KK, the productPlanetmathPlanetmath σ1σ2Gal(K/F) is the composite of the two maps σ1σ2:KK.

The Galois group of a polynomialPlanetmathPlanetmath f(x)F[x] is defined to be the Galois group of the splitting fieldMathworldPlanetmath of f(x) over F.

Title Galois group
Canonical name GaloisGroup
Date of creation 2013-03-22 12:08:19
Last modified on 2013-03-22 12:08:19
Owner djao (24)
Last modified by djao (24)
Numerical id 8
Author djao (24)
Entry type Definition
Classification msc 12F10
Related topic FundamentalTheoremOfGaloisTheory
Related topic InfiniteGaloisTheory