An A-hypergroup is obtained from a group G and from a non-empty subset A of G if one defines the hyperoperation as follows: for all (x,y)∈G×G , x∘y=xAy . This notion was introduced by T. Vougiouklis [Rend. Circ. Mat. Palermo (2) 36 (1987), no. 1, 114--121]. The author studies A -hypergroups obtained from abelian groups. After some general properties, the author analyses those of length 2 (i.e., for all (x,y) , |x∘y|=2) , finding some interesting results (such as Theorem 3.1); then he determines the number of the A-hypergroups obtainable from a cyclic finite group or from a group G such that |G|<12 .
Commutative Finite A-Hypergroups of Length Two Combinatorics ′86, Proceedings of the International Conference on Incidence Geometries and Combinatorial Structures
DE SALVO, Mario
1988-01-01
Abstract
An A-hypergroup is obtained from a group G and from a non-empty subset A of G if one defines the hyperoperation as follows: for all (x,y)∈G×G , x∘y=xAy . This notion was introduced by T. Vougiouklis [Rend. Circ. Mat. Palermo (2) 36 (1987), no. 1, 114--121]. The author studies A -hypergroups obtained from abelian groups. After some general properties, the author analyses those of length 2 (i.e., for all (x,y) , |x∘y|=2) , finding some interesting results (such as Theorem 3.1); then he determines the number of the A-hypergroups obtainable from a cyclic finite group or from a group G such that |G|<12 .File in questo prodotto:
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