Teorema de lagrange:

Abstract

Group Theory began in 1830 with Évariste Galois' discovery about the solvability of algebraic equations. This milestone was a reflection of centuries of studies and efforts of great mathematicians who, like Galois, sought to find a general method of solving polynomial equations of degree greater than five. Among many names that preceded and strongly contributed to the development of the theory is Joseph Louis Lagrange. The theory of groups has passed through several scholars throughout history, arriving in the way it is known in its modern statements and notations. In this sense, this paper is based on presenting and exemplifying key concepts and results of Group Theory to demonstrate the Lagrange Theorem, which deals with a relationship of the order of a group with the order of its subgroup and propose some applications in finite groups and in Number Theory, through the demonstration of Fermat's Little Theorem about divisibility by prime numbers.