Steiner triple systems with transrotational automorphisms (Q1332430)

A Steiner triple system of order \(v\) is said to be \(k\)-transrotational if it admits an automorphism consisting of a fixed point, a transposition and \(k\) cycles of length \((v-3)/k\). The author proves that a 1- transrotational Steiner triple system of order \(v\) exists if and only if \(v \equiv 1,7,9\) or \(15 \pmod {24}\) and that a 2-transrotational Steiner triple system of order \(v\) exists if and only if \(v \equiv 3\) or \(19 \pmod{24}\).