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New page: 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 "extensi...
The '''Galois group''' is a mathematical structure ([[group]]) associated to an 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 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.
[[Category:Algebra]]
Galois groups are named after [[Évariste Galois]], a [[French]] mathematician.
[[Category:Algebra]]