A Genelization of Subgroups

Group theory is an important branch of mathematics. It has important applications in many disciplines, such as in physics, chemistry and quantum mechanics. The aim of this document is to provide readers with a greater understanding of the basic knowledge of group theory. Specifically, firstly, the concepts and properties of different types of groups, subgroups and the definition of coset are introduced, which will be used in the next section. Besides, several examples including groups, finite groups, infinite groups, subgroups and abelian groups are listed. Then, a discussion of the two simple theorems and some lemmas will be showed so that readers can be familiar with the properties of groups. This discussion will deepen the understanding of maximal subgroups. This paper investigates the basic definitions and theorems of group theory. In the future, more researchers can pay attention to group theory and the application of group theory in more areas.