## Document Type

Honors Project

## First Advisor

Dr. James Bowling

## Degree Award Date

Spring 5-4-2024

## Keywords

Math, Groups, Group Theory, Lagrange, Abstract Algebra

## Disciplines

Algebra | Mathematics | Other Mathematics

## Abstract

Lagrange’s Theorem is a well-known result in group theory that many mathematicians consider to be one of the most important theorems relating to finite groups. This paper examines Lagrange’s Theorem and how it is utilized in the field of group theory. The theorem states that if G is a finite group and H is a subgroup of G, then the order of H divides the order of G. This paper will first cover elementary group theory terminology and concepts which provide context for a non-mathematical reader prior to proving Lagrange’s famous result. Then, it will explore derived consequences and applications of the theorem, namely Fermat’s Little Theorem and the Orbit-Stabilizer Theorem, that are heavily utilized when characterizing and analyzing different groups and their relations to subgroups to give the reader a complete understanding of the significance of Lagrange’s Theorem in finite group theory.

## Recommended Citation

Quinn, Kelsey Ann, "Lagrange's Theorem and its Applications in Group Theory" (2024). *Honors Projects*. https://digitalcommons.bridgewater.edu/honors_projects/

## Recommended Citation

Quinn, Kelsey Ann, "Lagrange's Theorem and its Applications in Group Theory" (2024). *Honors Projects*. https://digitalcommons.bridgewater.edu/honors_projects/