La R\'esolvante de Lagrange et ses Applications

TL;DR

This paper explores how group representation changes can be used to describe Galois groups of resolvent factors, leading to applications in algebraic Galois theory and pre-determination of Galois groups.

Contribution

It introduces a method using representation changes to analyze Galois groups of resolvent factors, providing new insights and applications in algebraic Galois theory.

Findings

Galois groups of resolvent factors can be pre-determined using representation theory.

The method applies to classical results in algebraic Galois theory.

New applications of Lagrange resolvents are demonstrated.

Abstract

In this paper, the changes of representations of a group are used in order to describe its action as algebraic Galois group of an univariate polynomial on the roots of factors of any Lagrange resolvent. By this way, the Galois group of resolvent factors are pre-determinated. In follows, different applications are exposed; in particular, some classical results of algebraic Galois theory.