TY - JOUR
T1 - 1-(v,3,r) designs and the equation x+y+z=0 in finite abelian groups
AU - Pavone, Marco
PY - 2009
Y1 - 2009
N2 - 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
AB - 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
KW - 1-designs
KW - finite abelian groups
KW - 1-designs
KW - finite abelian groups
UR - http://hdl.handle.net/10447/61014
M3 - Article
VL - II
SP - 171
EP - 175
JO - BOLLETTINO DI MATEMATICA PURA E APPLICATA
JF - BOLLETTINO DI MATEMATICA PURA E APPLICATA
ER -