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

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.