Embeddings of Resolvable Triple Systems

Let RB(3, λ; v) denote a resolvable λ-fold triple system of order v. It is proved in this paper that the necessary and sufficient conditions for the embedding of an RB(3, λ; v) in an RB(3, λ; u) are u⩾3v and (i) u≡v≡3 (mod 6) if λ≡1 (mod 2), (ii) u≡v≡3 (mod 3) if λ≡0 (mod 4), or (iii) u≡v≡0 (mod 3) and v≠6 if λ≡2 (mod 4). Necessary and sufficient conditions for the embeddings of resolvable directed triple systems are also determined for all λ.