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)...

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

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...

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...

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

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...

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...

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...

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...

said subgroups cannot be distinct. The inverse Galois problem: is every finite group the Galois group of a Galois extension of the rationals? Are there...

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...

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...

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

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

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...

equations of high degree. Évariste Galois coined the term "group" and established a connection, now known as Galois theory, between the nascent theory...

"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...

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...

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

percent-point function, inverse cumulative distribution function (after the cumulative distribution function or c.d.f.) or inverse distribution function...

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...

the inverse Galois problem over Q p ( t ) {\displaystyle \mathbb {Q} _{p}(t)} , and made many other significant contributions to the field of Galois theory...

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...

for Belyi functions, and has subsequently been much used in the inverse Galois problem. le Bruyn, Lieven (2008), Klein's dessins d'enfant and the buckyball...