86,945 research outputs found
Sigma theory for Bredon modules
We develop new invariants similar to the Bieri-Strebel-Neumann-Renz
invariants but in the category of Bredon modules (with respect to the class of
the finite subgroups of G). We prove that for virtually soluble groups of type
FP_{\infty} and finite extension of the Thompson group F the new invariants
coincide with the classical ones
Computation of Galois groups of rational polynomials
Computational Galois theory, in particular the problem of computing the
Galois group of a given polynomial is a very old problem. Currently, the best
algorithmic solution is Stauduhar's method. Computationally, one of the key
challenges in the application of Stauduhar's method is to find, for a given
pair of groups H<G a G-relative H-invariant, that is a multivariate polynomial
F that is H-invariant, but not G-invariant. While generic, theoretical methods
are known to find such F, in general they yield impractical answers. We give a
general method for computing invariants of large degree which improves on
previous known methods, as well as various special invariants that are derived
from the structure of the groups. We then apply our new invariants to the task
of computing the Galois groups of polynomials over the rational numbers,
resulting in the first practical degree independent algorithm.Comment: Improved version and new titl
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