FIT4.1. Galois Group of a Polynomial

EDIT: There was an in-video annotation that was erased in 2018. My source (Herstein) assumes characteristic 0 for the initial Galois theory section, so separability is an automatic property. Let's assume that unless noted. In general, Galois = separable plus normal. Field Theory: We define the Galois group of a polynomial g(x) as the group of automorphisms of the splitting field K that fix the base field F pointwise. The Galois group acts faithfully on the set of roots of g(x) and is isomorphic to a subgroup of a symmetric group. We also show that this action is transitive when g(x) is irreducible over F.