Galois theory: Abel's theorem
Channel: Richard E Borcherds
Date: 2021-01-08

This lecture is part of an online graduate course on Galois theory.

We discuss Abel's theorem, that says a general quintic equation cannot be solved by radicals. We do this by showing that if a polynomial can be solved by radicals over a field of characteristic 0 then its roots lie in a solvable Galois extension. We give some examples of degree 5 polynoimals whose roots do not generate a solvable extension.

The results about group theory used in the lecture are discussed in the group theory course https://www.youtube.com/playlist?list=PL8yHsr3EFj51pjBvvCPipgAT3SYpIiIsJ