特定阶的子群都同构且交换的有限p-群  

Finite p-groups whose subgroups of given order are all isomorphic and abelian

作　　者：赵立博[1] 郭秀云[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2013年第4期517-521,共5页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11071155)

摘　　要：研究某些子群同构的有限p-群是很有趣的.例如,Hermann和Mann都曾研究过极大子群都同构的有限p-群,但这类群的结构非常复杂,到现在人们都没能给出其分类.研究了特定阶的子群都同构且交换的有限p-群,并给出其分类.It is quite interesting to investigate finite p-groups in which some kind of subgroups are all isomorphic. For example, Hermann and Mann ever studied finite p-groups whose maximal subgroups are all isomorphic. However, it is dif- ficult to classify this kind of p-groups. In this paper, the finite p-groups whose subgroups given order are all isomorphic and abelian are investigated, and then the classification for this kind of groups is given.

关 键 词：AIi群 亚循环群 内亚循环群 内交换群 

分 类 号：O152.1[理学—数学]