Line-transitive point-imprimitive linear spaces with number of points being a product of two primes

The work studies the line-transitive point-imprimitive automorphism groups of finite linear spaces, and is underway on the situation when the numbers of points are products of two primes. Let S be a non-trivial finite linear space with cd points, where c and d are two primes. We prove that if G <= Aut(S) is line-transitive point-imprimitive, then G is solvable.