内交换p群的中心扩张(Ⅳ)

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

设N,H是任意的群.若存在群G,它具有正规子群≤Z(G),使得≌N且G/≌H,则称群G为N被H的中心扩张.本文完全分类了当N为p^3阶初等交换p群及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.从而我们完全分类了初等交换p群被内交换p群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 GIN ≈ H, then G is called a central extension of N by H. In this paper, we classified all groups which are central extensions of N by H, where N is an elementary abelian p-group of order p3 and H is an inner abelian p-group. Thus all groups which are central extensions of an elementary abelian p-group by an inner abelian p-group are classified.