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Group theory is the study of algebraic structures known as groups, which consist of a set of elements and an operation that combines them in a way that satisfies certain axioms. These structures arise naturally in many areas of mathematics and science, making group theory a fundamental part of pure mathematics. In the context of science and mathematics, group theory provides a powerful framework for understanding symmetry and its role in physical phenomena. It allows for the classification of geometric objects based on their symmetries, and it plays a central role in the study of quantum mechanics, where symmetry groups are used to describe the behavior of particles. In this way, group theory serves as a bridge between pure mathematics and the physical sciences, providing a common language for describing and understanding complex phenomena.