1831 Galois in the process of the solution of algebraic equations in the study,which was first a "group" of the term.and the conversion of group theory,algebraic equations to solve the problem.Study group on mankind emphasis way of thinking used to study the concept of the structure of the mode of thinking,This theory developed rapidly into a new branch of mathematics,on the formation and development of Modern Algebra had a tremendous impact,The scope and depth of the application of science and technology in various fields.The structure has been limited research is a hot group theory,theory has been completely resolved available for a limited group structure.and limited non-abelian group structure more complex.Theorem factor calculated using the same order of 200% for all types of groups.and the non-abelian group of 15 bands within the structure. 1831 Galois in the process of the solution of algebraic equations in the study,which was first a "group" of the term.and the conversion of group theory,algebraic equations to solve the problem.Study group on mankind emphasis way of thinking used to study the concept of the structure of the mode of thinking,This theory developed rapidly into a new branch of mathematics,on the formation and development of Modern Algebra had a tremendous impact,The scope and depth of the application of science and technology in various fields.The structure has been limited research is a hot group theory,theory has been completely resolved available for a limited group structure.and limited non-abelian group structure more complex.Theorem factor calculated using the same order of 200% for all types of groups.and the non-abelian group of 15 bands within the structure.