| Abstract: | 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 groupSym
e(G), the stabilizer of the identitye∈G in the groupSym(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
ofSym
e (G) constitute a lattice under ordinary join and meet and that the minimal elements of order two of this lattice is a subgroup
ofAut (G). |
