The concepts of group and symmetry * * * have their basic roots. Symmetry group defines the symmetry characteristics of geometric objects as consisting of a set of transformations that keep the object unchanged and operations that combine two such transformations in turn. This kind of symmetric group, especially continuous Lie group, plays an important role in many disciplines. For example, matrix group can be used to understand the basic physical laws of special relativity and the symmetry phenomenon in molecular chemistry.
The concept of group originated from the study of polynomial equations, which was developed by Evarist? Galois was founded in A.D. 1830, and the concept of group was formed and firmly established around A.D. 1870 after receiving contributions from other fields such as number theory and geometry. Modern group theory is a very active mathematics subject, which studies groups in its own way. In order to explore groups, mathematicians invented various concepts, and decomposed groups into smaller and better understood parts, such as subgroups, quotient groups, simple groups and so on. In addition to their abstract nature, group theorists also study various ways of expressing groups (group representation) from the perspective of theory and calculation. Developed a particularly rich theory of finite groups, which reached its peak in the classification of finite simple groups completed by 1983.