Let (G, +) be a finite abelian group with more than three elements and let B_3 be the family of all the unordered triples {x,y,z} of distinct elements of G such that x+y+z=0. We show that (G, B_3) is a 1-(v,3,r) design if and only if G is either an elementary abelian 3-group or the direct sum of Z/2Z with an elementary abelian 3-group. We also characterize the groups containing at least an element that does not belong to any triple in B_3
Pavone, M. (2009). 1-(v,3,r) designs and the equation x+y+z=0 in finite abelian groups. BOLLETTINO DI MATEMATICA PURA E APPLICATA, II, 171-175.
1-(v,3,r) designs and the equation x+y+z=0 in finite abelian groups
PAVONE, Marco
2009-01-01
Abstract
Let (G, +) be a finite abelian group with more than three elements and let B_3 be the family of all the unordered triples {x,y,z} of distinct elements of G such that x+y+z=0. We show that (G, B_3) is a 1-(v,3,r) design if and only if G is either an elementary abelian 3-group or the direct sum of Z/2Z with an elementary abelian 3-group. We also characterize the groups containing at least an element that does not belong to any triple in B_3
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