Research of Properties of Super Nilpotent Group

The research of nilpotent groups is a important part of the research of finite groups' theory.The research report of nilpotent groups is plentiful.Decribing properties of nilpotent groups is also difficult.As known,nilpotent groups G have a normal subgroups series:G = G1…Gr = 1 which makes Gi Gi + 1￡ Z(G Gi + 1)(i=1,2,…,r) discusses the generalization of nilpotent groups.Assumes that the factor group is super central and Gi Gi + 1 is cyclic group.According to it,intro duces a definition of super nilpotent groups.Discuss super nilpotent groups' properties with using the theory of finite groups,obtains some meaningful conclusions.