内交换p群的中心扩张(Ⅲ)

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

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^2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.

Assume N and H are groups.If there is a group G which has a normal subgroup ≤Z（G） such that ■N and G/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 an elementray abelian p-group of order p^2 and H is an inner abelian p-group.