| Applied Mathematics |
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| Construction of some hypergroups from combinatorial structures |
| Ali Reza Ashrafi, Ahmad Reza Eslami-Harandi |
| Department of Mathematics, Faculty of Science, University of Kashan, Kashan, Iran |
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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 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).
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Received: 15 September 2001
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