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. Whether thinking about Gf as a subgroup of Sn in this ...
