Sobre a caracterização de grupos abelianos finitamente gerados

Abstract

This work consists of a systematic study of Group Theory, starting from the definition of group and building the necessary theory for the proof of the Fundamental Theorem of Finitely Generated Abelian Groups. In addition, part of this work intends to study surrounding themes of the necessary path to reach the cited theorem, aiming to provide the reader with a theoretical basis for the understanding of such themes within Group Theory. Throughout the text, concepts are defined and results are proved within structural themes of the theory, such as groups and subgroups, homomorphisms, G-sets, p-groups, Sylow theorems, finite abelian groups, finite rank free abelian groups and finitely generated abelian groups.