Line-transitive automorphism groups of linear spaces
Summary: We prove the following theorem. Let \(S\) be a linear space. Assume that \(S\) has an automorphism group \(G\) which is line-transitive and point-imprimitive with \(k < 9\). Then \(S\) is one of the following: (a) a projective plane of order 4 or 7, (b) one of 2 linear spaces with \(v = 91\) and \(k = 6\), (3) one of 467 linear spaces with \(v = 729\) and \(k = 8\). In all cases the full automorphism group \(\text{Aut} (S)\) is known.
scientific article; zbMATH DE number 861591