RECOGNIZING GALOIS GROUPS Sn AND An

If f(X) ∈ K[X] is a separable irreducible polynomial of degree n and Gf is its Galois group over K (the Galois group of the splitting field of f(X) over K), then the group Gf can be embedded into Sn by writing the roots of f(X) as r1,..., rn and identifying each automorphism in the Galois group with the permutation it makes on the ri’s