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) , ...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) .展开更多
文摘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) .
