Resolvable group divisible designs with block size four and general index

In this paper, we investigate the existence of resolvable group divisible designs (RGDDs) with block size four, group-type h n and general index λ . The necessary conditions for the existence of such a design are n ≥ 4 , h n ≡ 0 ( mod 4 ) and λ h ( n − 1 ) ≡ 0 ( mod 3 ) . These necessary conditions are shown to be sufficient for all λ ≥ 2 , with the definite exceptions of ( λ , h , n ) ∈ { ( 3 , 2 , 6 ) } ∪ { ( 2 j + 1 , 2 , 4 ) : j ≥ 1 } . The known existence result for λ = 1 is also improved.