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).
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Ashrafi, A.R., Eslami-Harandi, A.R. Construction of some hypergroups from combinatorial structures. J. Zheijang Univ.-Sci. 4, 76–79 (2003). https://doi.org/10.1631/BF02841083
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DOI: https://doi.org/10.1631/BF02841083