Steiner triple systems with rotational automorphisms

A Steiner triple system S(υ) of order υ is said to be k-ratational (k positive integer) if it admits an automorphism consisting of a single fixed point and precisely k (υ−1)⧸k-cycles. We obtain a necessary and sufficient condition for the existence of 1-rotational and 2-rotational Steiner triple systems. We also enumerate nonisomorphic 1- and 2-rotational S(υ)'s of small orders.