grupa Galois

Nowadays they are still a fundamental tool to compute Galois groups.

See the article on Galois groups for further explanation and examples.

We can then find that this Galois group has a transposition.

This means that the number of elements in the associated Galois group is 1.

The absolute Galois group of an algebraically closed field is trivial.

No direct description is known for the absolute Galois group of the rational numbers.

However, for other solvable Galois groups, the form of the roots can be much more complex.

It is thus necessary to have a notion of Galois group for an infinite algebraic extension.

This means that the image of the Galois group in the representations is abelian.

This Galois group has only two elements: and the identity on .