Galois group
The Galois group Gal(K/F) of a field extension K/F is the group of all field automorphisms σ:K→K of K which fix F (i.e., σ(x)=x for all x∈F). The group operation
is given by composition: for two automorphisms
σ1,σ2∈Gal(K/F), given by σ1:K→K and σ2:K→K, the product
σ1⋅σ2∈Gal(K/F) is the composite of the two maps σ1∘σ2:K→K.
The Galois group of a polynomial f(x)∈F[x] is defined to be the Galois group of the splitting field
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 |