Category

Galois theory

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branch of mathematics that studies automorphism groups of fields

group of automorphisms of the Galois extension

Abel–Ruffini theorem

theorem that a generic equation of degree 5 or higher cannot be solved by radicals

Galois extension

algebraic field extension where the automorphism group fixes precisely the base field

sextic equation

polynomial equation of degree six

fundamental theorem of Galois theory

theorem that describes the structure of certain types of field extensions

Frobenius endomorphism

endomorphism of a commutative ring of non-zero characteristics

septic equation

mathematical equation

Newton's identities

relations between power sums and elementary symmetric functions

absolute Galois group

Galois group of the separable closure

Galois connection

pair of adjoint functors between two preordered sets seen as categories

quintic function

function defined by a polynomial of degree five

module over the group algebra of some Galois group

inverse Galois problem

unsolved problem in mathematics

differential Galois theory

study of Galois symmetry groups of differential fields

Galois cohomology

Group comohology of Galois modules

Artin–Schreier theory

in mathematics, a branch of Galois theory, and more specifically is a positive characteristic analogue of Kummer theory, for Galois extensions of degree equal to the characteristic p

Grothendieck–Teichmüller group

Mathematical group

radical extension

mathematical field obtained by adjunction of nth roots

Modular Elliptic Curves and Fermat's Last Theorem

concept in Galois theory