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Generalized Bhaskar Rao designs with block size 3 over finite abelian groups. (English) Zbl 1122.05011

Summary: We show that if \(G\) is a finite abelian group and the block size is \(3\), then the necessary conditions for the existence of a \((v,3,\lambda;G)\) GBRD are sufficient. These necessary conditions include the usual necessary conditions for the existence of the associated \((v,3,\lambda)\) BIBD plus \(\lambda \equiv 0 \pmod{|G|}\), plus some extra conditions when \(|G|\) is even, namely that the number of blocks be divisible by 4 and, if \(v = 3\) and the Sylow 2-subgroup of \(G\) is cyclic, then also \(\lambda \equiv 0 \pmod{2|G|}\).

MSC:

05B05 Combinatorial aspects of block designs
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