对偶超群

Dual Hypergroups

设 P( G)为群 G的幂集 ,则 P0 ( G) =P( G) -{ }关于运算 :AB+{ab|a∈ A,b∈ B}, A,B∈ P( G)作成一个半群 .若 Q≤ P( G)关于此运算为一个群 ,则称 Q为 G上的超群 .利用群 G的正规子半群的性质 ,将 G的幂集进行了完整地刻画 ,得到了单位群、对偶超群等概念 .并讨论了超群与对偶超群之间的关系 .

Let P(G)be power set of group G ,then P 0(G)=P(G)-｛｝ is a Semigroup about the operation:AB+｛ab｜a∈A,b∈B｝,B∈P(G)then Qis called a hypergroup over G.In this paper,we characterize the power set of a group G in terms of prope rties of normal subsemigroups,and get concepts of unit groups and dual hypergrou ps.This paper discusses the relationships between hypergroups and dual hypergrou ps.