Construction of some hypergroups from combinatorial structures  

作　　者：AliRezaAshrafi AhmadRezaEslami-Harandi 

机构地区：[1]DepartmentofMathematics,FacultyofScience,UniversityofKashan,Kashan,lran

出　　处：《Journal of Zhejiang University Science》2003年第1期76-79,共4页浙江大学学报（自然科学英文版）

摘　　要：Jajcay's studies( 1993 ; 1994) on the automorphism groups of Cayley maps yielded a new product of groups, which he called, rotary product. Using this product, we define a hyperoperation ⊙ on the group Syme (G) , the stabilizer of the identity e ∈ G in the group Sym (G) . We prove that ( Syme (G) , ⊙) is a hypergroup and characterize the subhypergroups of this hypergroup.Finally, we show that the set of all subhypergroups of Syme ( G ) constitute a lattice under ordinary join and meet and that the minimal elements of order two of this lattice is a subgroup of Aut (G) .Jajcay's studies(1993;1994) on the automorphism groups of Cayley maps yielded a new product of groups, which he called, rotary product. Using this product, we define a hyperoperation ⊙ on the group Sym e(G) , the stabilizer of the identity e∈G in the group Sym(G) . We prove that (Sym e(G) ,⊙) is a hypergroup and characterize the subhypergroups of this hypergroup. Finally, we show that the set of all subhypergroups of Sym e(G) constitute a lattice under ordinary join and meet and that the minimal elements of order two of this lattice is a subgroup of Aut(G) .

关 键 词：Finite group Rotary closed subgroup HYPERGROUP Sub  hypergroup Combinatorial structures 

分 类 号：O152[理学—数学]