| Let p be a prime.A group G is called a p-group if the order of its every element is a power of p.If the order of p-group G is finite,then G is called a finite p-group.Finite p-groups without any restriction except for their orders are,as usual,called the general finite p-groups.In this paper we survey the achievement of the classification in the general finite p-groups and the methods the classification used.The thesis consists four sections:In Section I,we introduce the history of the classi-fication of the p-groups which order is p"(n≤4),which contain the origin of the general finite p-groups classfication and some general methods used by the original scholars.In Section Ⅱ,we introduce the history of the classification of the p-groups which order is p5.In particular,we,using Magma,inspect the classification of orders 25 and p5(p≥3)respectively,which were given by M.Hall and R.K.James respectively.Moreover,we correct the errors of the classification of order p5 given by R.K.James.In Section Ⅲ,we introduce the history of the classification of the p-groups which order is p6.Lie methods and isoclinism is emphatically introduced briefly.Then we,using Magma,point out some errors of the classification of orders p6,which were given by R.K.James.In Section IV,we introduce the history of the classification of the p-groups which order is p7. |
