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 • Group theory
Негізгі бет Galois theory: Abel's theorem
Пікірлер: 12