El dual en grupos Abelianos finitos - Teorema de Pontryagin

Abstract

In the present graduate Monograph a first approximation is made to the duality theory about Finite abelian groups, distributed in 3 chapters: The first one contains the preliminaries about dual space from the algebraic point of view, that means in the vectors spaces and from the functional analysis point of view, in more general spaces like the normed spaces; definitions, theorems, corollaries and an entire collection of examples to understand the behaviour in dual space and subsequently to apply it into groups. In the second chapter is studied the convolution and the group algebra of a given group is created, also a very detailed description of its elements would be explained with examples and theorems which support the theory. In the third chapter we will introduce the duality in finite Abelian group’s topic, providing the group algebra presented in chapter two with a Hilbert´s space structure to subsequently talk about characters that will be of a great utility in the central theorem, Pontryagin's Duality Theorem for finite Abelian groups, at the end will be shown some examples which support the studied theory.