Central Extension Of Degree P Of Finite Metacyclic P-Groups

In this paper, we give a complete classification of the non-metacyclicp-groups G containing a normal subgroup N of order p such that G/N ismetacyclic.This paper consists of three chapters. ChapterⅠis an introductionto this paper. ChapterⅡgives a list of preliminaries for the paper. InChapterⅢ, we classify finite non-metacyclic p-groups containing a normalsubgroup N of order p such that G/N is metacyclic.