In this paper, we study the pro-Σ anabelian geometry of hyperbolic curves, where Σ is a nonempty set of prime numbers, over Galois groups of “solvably closed extensions” of number fields — i.e., infinite extensions of number fields which have no nontrivial abelian extensions. The main results of this paper are, in essence, immediate corollaries of the following three ingredients: (a) classical ...

We study the Ehresmann--Schauenburg bialgebroid of a noncommutative principal bundle as quantization gauge groupoid classical bundle. show that group is isomorphic to bisections bialgebroid, and we give crossed module structure for automorphisms bialgebroid. Examples illustrating these constructions include: Galois objects Taft algebras, monopole over quantum spheres not faithfully flat Hopf--G...

The Fibonacci-to-Galois transformation is useful for reducing the propagation delay of feedback shift register-based stream ciphers and hash functions. In this paper, we extend it to handle Galois-to-Galois case as well as feedforward connections. This makes possible transforming Trivium stream cipher and increasing its keystream data rate by 27% without any penalty in area. The presented trans...

Galois connection in crisp binary relations has proved to be useful for several applications in computer science. Unfortunately, data is not always presented as a crisp binary relation but may be composed of fuzzy values, thus forming a fuzzy binary relation. This paper aims at defining the notion of fuzzy galois connection corresponding to a fuzzy binary relation in two steps: firstly by defin...

— We study the structure of abelian subgroups of Galois groups of function fields.

We present a translation of §§160–166 of Dedekind’s Supplement XI to Dirichlet’s Vorlesungen über Zahlentheorie, which contain an investigation of the subfields of C. In particular, Dedekind explores the lattice structure of these subfields, by studying isomorphisms between them. He also indicates how his ideas apply to Galois theory. After a brief introduction, we summarize the translated exce...

We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. This constitutes the largest family of enumerative problems whose Galois groups have been largely determined. Using a criterion of Vakil and a special position argument due to Schubert, our result follows from a particular inequality among Kostka numbers of two-rowed tableau...

Résumé. L’approche présentée dans cet article a pour objectif la construction d’une ontologie à partir du treillis de l’iceberg de Galois. Nous entendons par ontologie un ensemble de termes structurés entre eux par un ensemble de liens de divers types. Dans notre cas d’étude, cette ontologie constitue un support de connaissances ”documentaires”. En effet, elle peut être utilisée dans diverses a...

We present a user interface, the OntoRefiner system, for helping the user to navigate numerous retrieved documents after a search querying a semantic portal which integrates a very important number of documents. Retrieved answers are filtered and the user could be provided only with the answers which are, according to him, the most relevant. The refinement process is based on two technologies, ...

If the absolute Galois group GK of a field K is a direct product GK = G1 × G2 then one of the factors is prosolvable and either G1 and G2 have coprime order or K is henselian and the direct product decomposition reflects the ramification structure of GK . So, typically, the direct product of two absolute Galois groups is not an absolute Galois group. In contrast, free (profinite) products of ab...