【摘要】 本文得到以下的结论:1.在G是有限群时,A是G的某一子群的商群。2.在G是无限群时,我们构造出A不是G的任何子群的商群的例子。3.A是G的商群的充要条件是:(ⅰ) (?)g∈G,存在A∈A,使得g∈A;(ⅱ)(?)A、B∈A,若A≠B,则A∩B=φ。更多还原

【Abstract】 In this paper, we discuss suck a group A, where every element is noempty subset of a group G and which operation is product of subset of G. The following results are obtained:(1) If G is finite, then A is a quotient group of a subgroup of G.(2) In case G is infinite, we construct an example of A, which is no quotient group of any subgroup of G.(3) is quotient group of G if and only if the following conditions are satisfied:(i) ?g∈G, there is an A∈A, such that g∈A. (ii) ?A, B∈A, if A≠B, then A∩B=φ,更多还原