关于广义四元数2-群的一个注记
A Note on Generalized Quaternion 2-Group
摘要:
运用有限p-群的有关知识，给出了两个判定广义四元数2-群的充要条件，进而得到结论：设G是一个有限p-群。则G的每个交换子群皆循环当且仅当G仅有一个p-阶子群。
Abstract:
This article uses the theory of the finite p-group, giving out two sufficiency and necessity conditions for the generalized quaternion 2-groups, thus obtaining the following conclusion: let G be a finite p-group. Then every abelian subgroup of G is cyclic if and only if G has only one subgroup of order p.
参考文献
|
[1]
|
徐明耀. 有限群导引(上册) [M]. 北京: 科学出版社, 1993: 55, 123-125, 154-158, 178.
|
|
[2]
|
Huppert, B. (1967) En-dliche Gruppen I. Springer-Verlag, Berlin, Heidelberg, New York. [Google Scholar] [CrossRef]
|
|
[3]
|
陈彦恒, 曹洪平. 各阶非平凡子群的个数为p + 1的p-群的完全分类[J]. 西南大学学报(自然科学版), 2007, 29(2): 11-14.
|