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.

[Tadesan]

You are like a freight train. The math just keeps coming! Love it!

[scin]

Thanks for your work. Really great service to the community!

[romainmp]

great! so much in so little time! and still clear!

[SuperYtc]

This Galois theory is very tough to get your head around...

[sapuszchkyn]

thanks! I'm going to be examed from Galois theory next week  :)

[senkakutenanmon]

Mr. Bob if you allow me to add to your explanation,
the order of symmetric group = deg(g(x)),
g(x) is assumed to be separable.

[hansisbrucker]

Some things I can recognize from Category Theory, but those orbits flew right over my head 😅

[MathDoctorBob]

Shazam, shazam, shazam! I couldn't imagine trying to teach Pyle Abstract Algebra.

[therealpekka]

very good, that helped a lot :) thanks