10.18453/rosdok_id00005896 Grüttmüller, Martin Martin Grüttmüller http://d-nb.info/gnd/122522559 Rees, Rolf S. Rolf S. Rees http://d-nb.info/gnd/122169727 Shalaby, Nabil Nabil Shalaby University of Rostock, Institute of Mathematics 2005 510 Mathematics 2005 en https://purl.uni-rostock.de/rosdok/id00005896 urn:nbn:de:gbv:28-rosdok_id00005896-0 In this paper we investigate exhaustively the cyclically indecomposable triple systems TSλ(v) for λ = 2, v ≤ 33 and λ = 3, v ≤ 21 and we identify the decomposable ones. We also construct, by using Skolem-type and Rosa-type sequences, cyclically indecomposable two-fold triple systems TS2(v) for all admissible orders. Further, we investigate exhaustively all cyclic TS2(v) that are constructed by Skolem-type and Rosa-type sequences up to v ≤ 45 for indecomposability.