幂群与它的生成群

设г是G上的幂群,即以G的非空子集为元素,在G的子集的运算之下所成的群.P_1,P_2是这样的两个性质 P_1:对任意g∈G,存g∈G,存在A∈г,使得g∈A. P_2:对任意A,B∈г,如果A≠B,则A∩B=φ. 本文得出了群G上的幂群г分别具有性质P_1或P_2的充要条件.

Power Groups and Their Generating Groups

Let T be, a power group on G, that means all elements of T are, subsets of G and the operation is subset product of G. Let P1 and P2 be two properties of power groups defined as followingP1 : for all g ∈ G, there exits A ∈ T, such that g ∈ A.P2 : for all A, B ∈ T, if A ≠ B then 4 ∩ 5 =φ.The sufficient and necessary conditions for a power group to have each property P1 or P2 are abtained in this paper.