Steiner triple systems with near-rotational automorphisms

AbstractA Steiner triple system of order v, denoted STS(v), is said to be k-near-rotational if it admits an automorphism consisting of three fixed points and k cycles of length (v − 3)k. In this paper, we show that, for n ⩾ 1, a 2n-near-rotational STS(v) exists if and only if v ≡ 1 or 3 (mod 6), v ≡ 3 (mod 2n), and v ≠ 13 or 21 when n = 1. Also, for n ⩾ 1, a 3n-near-rotational STS(u) exists if and only if v ≡ 3 (mod 6) and v ≡ 3 (mod 3n)