作　　者： ;

机构地区： 北京师范大学数学科学学院

出　　处： 《Chinese Quarterly Journal of Mathematics》 1990年第4期102-106,共5页

摘　　要： §1 预备知识为了使本文自成一体,先介绍一些必备的定义和定理。定义1.1 设G是一个群,在(G)\{}中引入代数运算:A·B={a·b|a∈A,b∈B}。如果一个非空集族((G)\{(}对上运算作成群,我们称为G上幂群,其单位元用E来表示。定义1.2 设为幂群,若e∈E,其中e为G中单位元,则称为G的正则幂群。定理1.1 如果为G上的一个幂群,用|A|表示A的元素个数。 The problem of upgrade has been emphsised with the development of fuzzy mathematics. The problem of upgrade on algebraic structure was considered in paper[1], and the concept of the hypergroup was raised, And then, the works were carried out in the paper [2]—[6]. This paper gives some further description for hypergroup. The main work is concluded as follows: (1) Solving the structure of hypergroup on the cyclical group. (2)Relationship amang the associative hypergroups for group, normal subgroup and factor group is considered. (3)Relationship between hypergroup and ordinary group is descriped. (4)The problem of existence on maximal, maximun, minimun element for the hypergroup which satisfys certain restricted condition is considered.

关 键 词： 幂群 一致幂群 正规子群 商群 直积

领　　域： [理学] [理学]