奇数阶亚循环p-群分类的一个证明

摘要

A finite p-group P is called metacyclic if it has a cyclic normal subgroup A such that P/A is cyclic. King[2] classified metacyclic p-groups. M.F. Newman and Ming-yao Xu developed a new approach to metacyclic p-groups suggested by a pgroup generation algorithm they found new representations for these groups[3-5].This paper gives another proof of these results, independent of the p-group generation algorithm.%一个有限p-群p称为亚循环的,如果P有一个循环的正规子群A,使得P/A是循环的.1973年King在文[2]中对亚循环p-群进行了分类;在文[4,5]中M.F.Newman and ing-Yao Xu发现了这些群的新的表示,给出了新的分类方法,这种方法是由p-群生成算法(见文[3])得到的.本文的目的是给这些结果的另一种证明,与p-群生成算法是不相关的.