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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, including lattice theory, where they can be used to describe the symmetry of lattices and other mathematical objects. In group theory, one studies the properties of groups, such as their subgroups, homomorphisms, and automorphisms, as well as the ways in which groups can be combined or factored into smaller groups. This field has many applications in mathematics, physics, and computer science, and it plays a central role in the study of symmetry and structure in these disciplines.