Galois group

== English == === Etymology === Named after Évariste Galois, who first discovered them. === Noun === Galois group (plural Galois groups) (algebra, Galois theory) The automorphism group of a Galois extension. ==== Usage notes ==== The automorphism group of a Galois extension L / K {\displaystyle L/K} may be denoted Gal ( L / K ) {\displaystyle {\mbox{Gal}}(L/K)} . Gal ⁡ ( F / F ) {\displaystyle \operatorname {Gal} (F/F)} is the trivial group whose single element is the identity automorphism. ==== Translations ==== === See also === Galois algebra Galois closure Galois extension Galois theory === Further reading === Galois theory on Wikipedia.Wikipedia Galois closure on Wikipedia.Wikipedia Galois extension on Wikipedia.Wikipedia