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|).
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
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|).
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