Computation of Galois groups and applications: degree 24 and more
by
Claus Fieker
University of Sydney, Magma-Group
Coauthors: Jürgen Klüners

The computation of Galois groups is one of the oldest tasks in computational algebra. Originally developed to decide solvability of polynomial equations, it quickly matured into an independent branch of research. While a trivial argument shows that Galois groups can be computed in finite time, a practical algorithm in the genral case was still missing. Since Stauduhars thesis in 78, the problem has been solved degree by degree and thesis by thesis, until it reached 23 by 2004. Over the last 2 years, we managed to remove the degree limitation from the algorithm, resulting in an unlimited practical method.

In this talk I will explain how we succeeded to remove the degree limitation. Furthermore, applications, such as solvability be radicals, will be discussed.

Date received: March 18, 2009