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Group theory is the study of algebraic structures known as groups, which consist of a set of elements equipped with an operation that combines any two of its elements to form a third element in such a way that four conditions called group axioms are satisfied. It is a fundamental area of mathematics that has applications in many other areas, including physics, chemistry, and computer science. In the context of algebraic geometry, group theory plays a crucial role in the study of symmetry groups of geometric objects, providing a powerful tool for understanding their structure and properties. It also has important connections to number theory and topology, making it a central area of study in mathematics.