Group theory
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Group theory is the study of mathematical groups, including their symmetries and permutations. It has applications in science, and became one of the most active branches in all of mathematics in the 20th century.
There are three main sources of group theory. The first source of group theory was number theory, beginning in the late 1700s. A second source was the theory of algebraic equations, leading to the study of permutations, also beginning in the late 1700s. A third source of group theory was geometry beginning around 1800.