Lecture 20. Galois Groups and Reduction mod p

0:00 Transitive action of the Galois group on a set of prime ideals
12:46 Integral elements in the Galois extension
27:10 Example: integral elements in Q[sqrt(5)].
29:48 Dedekind Theorem: information about the Galois group from the reduction mod p
50:35 Example: Galois group of a polynomial of degree 4
55:27 A useful Lemma about the group of permutations

In this lecture we prove Dedekind's Theorem that relates Galois groups of polynomials over Q to their reductions mod p.

This is a lecture in a graduate course "Groups and Galois Theory".

Here is the complete playlist for this course: