SYMMETRIC GROUPS

Abstract

In this project, we delve into the applications, examples, and prominent theories surrounding symmetric groups. Each element in a symmetric group represents a bijection of the set onto itself, and the group operation involves function composition. We will begin by outlining the concept of symmetry through a few fundamental examples and applications. Following this, we will introduce some real-world applications, providing a clear definition and understanding. Next, we will explore properties and notable elements of symmetric groups. Finally, we will analyze the subgroup structure of symmetric groups and present some representative theoretical frameworks.