Generalized Bhaskar Rao Designs with Block Size 3 over Finite Abelian Groups.

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,λ; G) GBRD are sufficient. These necessary conditions include the usual necessary conditions for the existence of the associated ( v,3,λ) BIBD plus λ≡ 0 (mod| 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 λ≡ 0 (mod2| G|). [ABSTRACT FROM AUTHOR]