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Received: 2001-09-15

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Journal of Zhejiang University SCIENCE A 2003 Vol.4 No.1 P.76-79


Construction of some hypergroups from combinatorial structures

Author(s):  Ali Reza Ashrafi, Ahmad Reza Eslami-Harandi

Affiliation(s):  Department of Mathematics, Faculty of Science, University of Kashan, Kashan, Iran

Corresponding email(s):   ashrafi@kashanu.ac.ir

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

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Ali Reza Ashrafi, Ahmad Reza Eslami-Harandi. Construction of some hypergroups from combinatorial structures[J]. Journal of Zhejiang University Science A, 2003, 4(1): 76-79.

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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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