Steiner Triple Systems with Automorphism Type \([1,0,0,0,0,0,0,t,0,…,0,1,0,…,0]\)

Abstract

Necessary and sufficient conditions are given for a Steiner triple system of order \(t\) admitting an automorphism consisting of one large cycle, cycles of length \(8\), and a fixed point, with \(t \leq 4\). Necessary conditions are given for all \(t \geq 1\).