Talde abeldar finituetarako Galoisen alderantzizko problema

Abstract

The inverse Galois problem wonders about the question whether any given finite group is isomorphic to the Galois group of a Galois extension. In this article, we will prove the Kronecker-Weber theorem, or in other words, that any abelian finite group is isomorphic to the Galois group of a Galois extension over Q: In this article, a number of concepts and brush-strokes of the necessary results to supportthis proof will be mentioned and presented: first, certain fundamental results of algebra, corresponding to polynomials and congruences; then, the fundamental definitions and theorems of Galois theory, and some notes of cyclotomic extensions; and finally, Kronecker-Weber theorem will be enunciated and proved, taking into account all the previous results.