两类具有N_p-序列有限p-群之增广商群的结构

On Structure of an Augmentation Quotient Group with N_p-Series

应用具有Np-序列有限p-群的特殊性质和重量函数,基本序列等概念以及已有的一些结果,分别研究了类为1的pk(k 2)阶A bel基本p-群和类为2的p4阶基本p-群之增广商群Qn(G)的结构,得到了当n足够大时Qn(G)作为A bel基本p-群的秩。

Theorem 1 in this paper is taken from the paper by G. Losey and N. Losey. We consider Theorem 1 to be highly significant and apply it to obtaining the rank of a certain augmentation quotient group by proposing Theorem 3 and giving its complete proof. We now state Theorem 3 as follows ： ＂Let G be nonabelian elementatry finite p-group （p prime, p≠2） with order p^4, and let H be Np-series of G with t1=3, t2=l, c=2. Then, Qn（G） is an abelian elementary p-group with rank 1/2（p＋1）（p^2＋p＋1） for all n≥p-2.