mathematics In Galois theory, the inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of...

In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection...

In mathematics, the absolute Galois group GK of a field K is the Galois group of Ksep over K, where Ksep is a separable closure of K. Alternatively it...

Galois module Galois representation Galois ring Galois theory Differential Galois theory Topological Galois theory Inverse Galois problem Galois (crater)...

precisely which finite groups occur as Galois groups over K . {\displaystyle K.} This is the inverse Galois problem for a field  K . {\displaystyle K.} (For...

polynomial for a given Galois group provides a complete solution to the inverse Galois problem for that group. However, not all Galois groups have generic...

curves. Their rational points are of interest for the study of the inverse Galois problem, and as such they have been extensively studied by arithmetic geometers...

describing predatory interactions between competing species Inverse Galois problem, an open problem in mathematics This disambiguation page lists articles...

inverse Galois problem, Hilbert's original motivation. The theorem almost immediately implies that if a finite group G can be realized as the Galois group...

In Galois theory, a branch of mathematics, the embedding problem is a generalization of the inverse Galois problem. Roughly speaking, it asks whether...

subgroups of the Galois group. In 1918, Noether published a paper on the inverse Galois problem. Instead of determining the Galois group of transformations...

distinct. The inverse Galois problem: is every finite group the Galois group of a Galois extension of the rationals? Isomorphism problem of Coxeter groups...

named by Matzat (1987). It appears in Galois theory, in the study of the inverse Galois problem or the embedding problem which is a generalization of the former...

strands being on the sphere. The group also has relations to the inverse Galois problem. The spherical braid group on n strands, denoted S B n {\displaystyle...

she focused on aspects of Galois theory, including Galois groups, geometric Galois actions, and the inverse Galois problem, and has been described by...

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any...

the Galois group Gal ⁡ ( K / k ) {\displaystyle \operatorname {Gal} (K/k)} . This interpretation of the Galois group is known as Grothendieck's Galois theory...

also made major contributions to the inverse Galois problem. He found a criterion for a finite group to be a Galois group, that in particular implies that...

instead of complex numbers. The algebraic solution of this problem allows the use of Galois theory to prove that, for certain easily constructed inputs...

the Galois groups of global fields are not known. Inverse Galois theory studies the (unsolved) problem whether any finite group is the Galois group...

between various algebraic K-theory groups. Rigid groups in the inverse Galois problem. In combinatorics, the term rigid is also used to define the notion...

Formally real field Real closed field Applications Galois theory Galois group Inverse Galois problem Kummer theory General Module (mathematics) Bimodule...

Évariste Galois in the 1830s, who introduced the term group (French: groupe) for the symmetry group of the roots of an equation, now called a Galois group...

referred to as differential Galois theory, by analogy with algebraic Galois theory. The basic theorem of differential Galois theory is due to Joseph Liouville...

"Teichmüller's Lego-game and the Galois group of Q over Q" ("Un jeu de “Lego-Teichmüller” et le groupe de Galois de Q sur Q"). 3. Number fields associated...

question is what G can be. This is therefore a special type of inverse Galois problem. The subgroup p(G) is defined to be the subgroup generated by all...

Galois theory is a result that describes the structure of certain types of field extensions in relation to groups. It was proved by Évariste Galois in...

field of rational numbers play also an important role in solving inverse Galois problems. Given any algebraic function field K over k, we can consider the...

statement. This conjecture would imply a positive answer to the inverse Galois problem. Serre (1992) p.26 Serre (1992) p.27 Serre (1992) p.19 Schinzel...

Schneps, Leila; Lochak, Pierre, eds. (1997), Geometric Galois actions II. The inverse Galois problem, moduli spaces and mapping class groups. Proceedings...