Construction of some hypergroups from combinatorial structures

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 [symbol: see text] on the group Syme(G), the stabilizer of the identity e [symbol: see text] G in the group Sym(G). We prove that (Syme(G), [symbol: see text]) 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).