Difference between revisions of "Galois group"
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| − | + | The '''Galois group''' is a mathematical structure ([[Group (mathematics)|group]]) associated to an [[field extension|extension of field]]s. Given two fields E and F where F (the "base field") is contained in E (the "extension field"), we define Gal(E/F) to be the set of [[automorphism]]s of E which fix F. The Galois group of a [[polynomial]] f over a field F is the Galois group associated to F(α) where α is a [[root]] of f. The group obtained does not depend on the choice of root. | |
| − | Galois groups | + | Galois groups are named after [[Évariste Galois]], a [[French]] [[mathematician]]. |
| − | [[ | + | [[Category:Algebra]] |
Latest revision as of 04:21, November 11, 2011
The Galois group is a mathematical structure (group) associated to an extension of fields. Given two fields E and F where F (the "base field") is contained in E (the "extension field"), we define Gal(E/F) to be the set of automorphisms of E which fix F. The Galois group of a polynomial f over a field F is the Galois group associated to F(α) where α is a root of f. The group obtained does not depend on the choice of root.
Galois groups are named after Évariste Galois, a French mathematician.