Embeddings and Prescribed Intersections of Transitive Triple Systems

Two problems concerning transitive triple systems (TTS s ) are discussed. It is shown that if u, ν ≡ 0 or 1 (mod 3) and u ≥ 2ν + 1, then there exists a TTS of order u containing a TTS of order v as a subsystem; and for every ν ≡ 0 or 1 (mod 3) there exists a pair of TTS s of order ν intersecting in exactly κ triples, for any κ in the range 0 ≤ κ ≤ ν(ν - 1)/3 except precisely κ = ν(ν-1)/3-1.