O teorema da correspondência de grupos

Abstract

The Correspondence Theorem for Groups is one of the fundamental pillars in group theory, a central area of abstract algebra. The primary goal of this work is to explore and present a detailed understanding of the Correspondence Theorem, covering essential concepts such as group homomorphisms, normal subgroups, and quotient groups. Initially, basic concepts of abelian and non-abelian groups are introduced, followed by an in-depth analysis of group homomorphisms and their properties. Next, Lagrange's Theorem is discussed, establishing the basis for the introduction of normal subgroups and quotient groups. The work culminates in the demonstration and application of the Correspondence Theorem, highlighting its theoretical and practical importance. The research was based on an extensive bibliographic review, utilizing renowned sources in the field of mathematics. The results obtained reinforce the relevance of the Correspondence Theorem in the structure of group theory and its applicability in various areas of mathematics.