Until the 1990’s the only known finite linear spaces admitting line-transitive, pointimprimitive groups of automorphisms were Desarguesian projective planes and two linear spaces with 91 points and line size 6. In 1992 a new family of 467 such spaces was constructed, all having 729 points and line size 8. These were shown to be the only linear spaces attaining an upper bound of Delandtsheer and...

With the exception of Hering’s plane of order 27, all known odd order flag-transitive a‰ne planes are one of two types: admitting a cyclic transitive action on the line at infinity, or admitting a transitive action on the line at infinity with two equal-sized cyclic orbits. In this paper we show that when the dimension over the kernel for these planes is three, then the known examples are the o...

For a graph Γ, subgroups M < G 6 Aut(Γ), and an edge partition E of Γ, the pair (Γ, E) is a (G, M)-homogeneous factorisation if M is vertex-transitive on Γ and fixes setwise each part of E , while G permutes the parts of E transitively. A classification is given of all homogeneous factorisations of finite Johnson graphs. There are three infinite families and nine sporadic examples.

We study the middle convolution of local systems on the punctured affine line in the singular and the étale case. We give a motivic interpretation of the middle convolution which yields information on the occurring determinants. Finally, we use these methods to realize special linear groups regularly as Galois groups over Q(t). Introduction If K is a field, then we set GK := Gal(K/K), where K d...

This paper is devoted to the classification of flag-transitive 2-(v,k,2) designs. We show that apart from two known symmetric 2-(16,6,2) designs, every subgroup G automorphism group a nontrivial design primitive affine or almost simple type. Moreover, we classify designs admitting flag transitive with socle PSL(n,q) for some n≥3. Alongside this analysis give construction 2-(v,k−1,k−2) given 2-(...

This note is part of a general programme to classify the automorphism groups of nite linear spaces. There have been a number of contributions to this programme including two recent surveys, 8, 3]. One of the most signiicant contributions was the classiication of ag-transitive linear spaces, 1]. Since then the eeort has been to classify the line-transitive examples. These fall naturally into two...

The group of projectivities of (a line of) a projective plane is always 3-transitive. It is well known that the projective planes with a sharply 3-transitive group of projectivities are classi/ed: they are precisely the Pappian projective planes. It is also well known that the group of projectivities of a generalized polygon is 2-transitive. Here, we classify all generalized quadrangles, all /n...

This note is part of a general programme to classify the automorphism groups of finite linear spaces. There have been a number of contributions to this programme, including two recent surveys [8, 3]. One of the most significant contributions was the classification of flag-transitive linear spaces [2]. Since then, the effort has been to classify the line-transitive examples. These fall naturally...

The groups in the title are classified, provided they are not too highly transitive. Let G be a primitive permutation group on a finite set S of n points. In 1871, Jordan initiated the study of G under the additional assumption that there is a transitive subgroup H of degree m, where 1 < m < n; that is, H fixes n m points and is transitive on the remaining points. THEOREM 1. I f m is a prime po...

This result has been refined considerably by a number of authors. Wietandt and Huppert [14] introduced the notion of multiple primitivity and (t+ 89 transitivity. Wagner [13] showed that H is in fact t-fold transitive if n t is an even number and t > 3, and Saxl [8] proved that this is also true if t > 4 and n < 106. The only known examples of triply transitive groups with only doubly transitiv...