内交换p群的中心扩张(Ⅱ)

The Central Extension of Inner Abelian p-Groups(Ⅱ)

设N,H是任意的群.若存在群G,它具有正规子群N≤Z(G),使得N≌N且G/N≌H,则称群G为N被H的中心扩张.本文完全分类了当N为循环p群,H为内交换p群时,N被H的中心扩张得到的所有不同构的群.

Assume N and H are groups. If there is a group G which has a normal subgroup N^-≤Z（G） such that N^- ≈N and G/N^- ≈H, then G is called a central extension of N by H. In this paper, we classify all groups which are central extensions of N by H, where N is a cyclic p-group and H is an inner abelian p-group.