Line-primitive automorphism groups of finite linear spaces (Q1822762)

Let S be a finite linear space. Let G be a group of automorphisms of S acting primitively on the b lines of S. Theorem 1. If S is not a projective plane, then G is almost simple, i.e. there is a non-abelian simple group T of order \(>b\) such that \(T\leq G\leq Aut T.\) Theorem 2. If S has \(line\)-size\(<30\), then G acts primitively on the points of S.