Some progress on the existence of 1-rotational Steiner triple systems (Q663467)

A Steiner triple system is \textsl{1-rotational under group} \(G\) if it has \(G\) as an automorphism group acting sharply transitively on all but one point. Complete existence results are known when \(G\) is cyclic, abelian, or dicyclic. This paper addresses cases when \(G\) is arbitrary, and obtains a complete existence result except when \(v \equiv 1 \pmod{96}\), \(v = (p^3-p)n +1\) for \(p\) a prime, \(n \not\equiv 0 \pmod{4}\), and the odd part of \((p^3-p)n\) is square-free and has no prime factors that are congruent to 1 modulo 6.