
112 The Idea Behind Galois Theory
tions between them turns out to be the symmetry group of the subfield Q(α, β ,γ,δ )
of C generated by the zeros of g, or more precisely its automorphism group, which
is a fancy name for the same thing.
Moreover, we wish to consider polynomials not just with integer or rational co-
efficients, but coefficients that lie in a subfield K of C (or, later, any field). The zeros
of a polynomial f (t) with coefficients in K determine another field L which contains
K, but may well be larger. Thus the primary object of consideration is a pair of fields
K ⊂ L, or in a slight generalisation, a field extension L : K. Thus when Galois talks ...