Let L be an extension field of K, denoted L/K, and let G be the set of automorphisms of L/K, that is, the set of automorphisms σ of L such that σ(x) = x for every x element K, so that K is fixed. Then G is a group of transformations of L, called the Galois group of L/K. The Galois group of L/K is denoted Gal(L/K) or Aut(L/K).

Abhyankar's conjecture | finite group | fundamental theorem of Galois theory | Galois's theorem | Galois theory | group | solvable group | symmetric group

Évariste Galois