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)...

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

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...

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

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...

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

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...

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...

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

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...

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

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...

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...

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...

"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...

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

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

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...

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

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...

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...

S2CID 5317997. Yun, Zhiwei (2014). "Motives with exceptional Galois groups and the inverse Galois problem". Inventiones Mathematicae. 196 (2): 267–337. arXiv:1112...

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

vanish. The inverse Galois problem seems to be unsolved for M23. In other words, no polynomial in Z[x] seems to be known to have M23 as its Galois group. The...