In mathematics, groups represent algebraic structures with binary operations satisfying closures, associative laws, identity elements and inverses, including Abel groups, homomorphisms and * * * yokes. A finite group is a group with finite elements. One of the important contents of group theory. The number of elements it contains is called the order of finite groups. Finite groups can be divided into two categories: solvable groups and unsolvable groups (especially noncommutative simple groups) (see groups and finite simple groups). Finite group theory is the basic part of group theory and the most widely used branch of group theory. Historically, many concepts of abstract group theory originated from finite group theory. In recent years, with the rapid development of finite group theory and its increasingly extensive application, finite group theory has become one of the mathematical foundations of modern science and technology, and it is also a mathematical tool that ordinary scientific and technological workers are willing to master. Finite group theory occupies a prominent position both in theory itself and in practical application. Its permutation group, solvable group and insoluble group, nilpotent group and group representation theory are all important research objects. In a word, its content is very rich and huge.