Galois group

Noun

Meaning

Galois group (plural Galois groups)

(algebra, Galois theory) The automorphism group of a Galois extension.

Examples

Specifically, the Galois group of F over E, denoted Gal(F/E), is the group of field automorphisms of F that are trivial on E (i. Source: Internet

The Galois group of every finite extension of a finite field is finite and cyclic, with an iterate of the Frobenius endomorphism as its generator. Source: Internet

Since the Galois group of the general quintic equation is isomorphic to the symmetric group on five letters, and this normal subgroup is simple and non-abelian, the general quintic equation does not have a solution in radicals. Source: Internet

Every polynomial equation in one variable has a Galois group, that is a certain permutation group on its roots. Source: Internet

He realized that the algebraic solution to a polynomial equation is related to the structure of a group of permutations associated with the roots of the polynomial, the Galois group of the polynomial. Source: Internet

In this case, the group that exchanges the two roots is the Galois group belonging to the equation. Source: Internet

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