Inverse Galois problem information

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...

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...

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...

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...

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...

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...

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

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 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...

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

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

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...

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

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...

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...

then F has an inverse function G: kN → kN which is regular, meaning its components are polynomials. According to van den Essen, the problem was first conjectured...

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...

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

the rational numbers are Hilbertian. Results are applied to the inverse Galois problem. Thin sets (the French word is mince) are in some sense analogous...

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...