奇数阶亚循环p-群分类的一个证明(英文)

A proof of classification of metacyclic p-groups for odd p

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PA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.NewmanandMingYaoXu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.

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 p group 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.