Transitive projective planes and 2-rank

Sharply 2-transitive groups of projectivities in generalized polygons

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...

A Geometric Characterization of Fischer's Baby Monster

The sporadic simple group F2 known as Fischer's Baby Monster acts flag-transitively on a rank 5 P-geometry G(F2). P-geometries are geometries with string diagrams, all of whose nonempty edges except one are projective planes of order 2 and one terminal edge is the geometry of the Petersen graph. Let AC be a flag-transitive P-geometry of rank 5. Suppose that each proper residue of K is isomorphi...

Flag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups

The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).

FINITE s-ARC TRANSITIVE CAYLEY GRAPHS AND FLAG-TRANSITIVE PROJECTIVE PLANES

In this paper, a characterisation is given of finite s-arc transitive Cayley graphs with s ≥ 2. In particular, it is shown that, for any given integer k with k ≥ 3 and k 6= 7, there exists a finite set (maybe empty) of s-transitive Cayley graphs with s ∈ {3, 4, 5, 7} such that all s-transitive Cayley graphs of valency k are their normal covers. This indicates that s-arc transitive Cayley graphs...

Transitive hyperovals in finite projective planes