The author calls a hypergroup of constant length n , a hypergroup H such that for all (x,y)∈H×H , |x∘y|=n . In the first part of the paper, some interesting properties of these hypergroups (in the finite case) are found. In the second part, all commutative hypergroups of order 3 and length 2 are determined, making use of a computer program to verify associativity. For this program see a paper by R. Migliorato [in Hypergroups, other multivalued structures and their applications (Italian) (Udine, 1985), 131--136, Univ. Studi Udine, Udine, 1985; see MR0923141 (88g:20004)].
Finite hypergroups of constant length
DE SALVO, Mario
1986-01-01
Abstract
The author calls a hypergroup of constant length n , a hypergroup H such that for all (x,y)∈H×H , |x∘y|=n . In the first part of the paper, some interesting properties of these hypergroups (in the finite case) are found. In the second part, all commutative hypergroups of order 3 and length 2 are determined, making use of a computer program to verify associativity. For this program see a paper by R. Migliorato [in Hypergroups, other multivalued structures and their applications (Italian) (Udine, 1985), 131--136, Univ. Studi Udine, Udine, 1985; see MR0923141 (88g:20004)].File in questo prodotto:
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