Advances in International Applied Mathematics

Group theory, as an important branch of mathematics, has always been the focus of the mathematical community for its historical context, development trajectory and frontier exploration. Since the birth of group theory, it has experienced a course from the construction of basic theory to the wide application of modern mathematics, and then to the in-depth exploration of frontier fields. In this process, group theory not only provides powerful tools and methods for mathematical research, but also provides important support for the development of other scientific fields. In the development of group theory, many outstanding mathematicians have made outstanding contributions to it. In modern mathematics, the application of group theory has penetrated into various branches. For example, in algebraic geometry, group theory is used to study the symmetries and transformation properties of geometric objects, providing new perspectives and methods for the development of geometry. In topology, group theory is used to study the continuous transformation and topological structure of space, which provides a powerful tool for the study of topology. In addition, in number theory, quantum mechanics, cryptography and other fields, group theory also plays an important role. These applications not only demonstrate the wide applicability of group theory, but also further promote the development of group theory. With the continuous progress of science and technology and the in-depth development of mathematical research, the application field of group theory will be more extensive, and its theoretical system will continue to improve and innovate.

Group theory; Math; Apply