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 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).

Key words: Finite group, Rotary closed subgroup, Hypergroup, Sub-hypergroup, Combinatorial structures

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