Concerning extended triple systems with rotational automorphisms - Jiang, Zhike,; McLeish, Mary, (Utilitas Mathematica, 1999)
An extended triple system of order v is said to be k-rotational if it admits an automorphism which consists of a single fixed point and precisely k cycles of length (v - 1)/k. We obtain a necessary and sufficient condition for the existence of 3-and 4-rotational extended triple systems.