Transitive projective planes and insoluble groups

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).

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...

Finite line-transitive linear spaces: parameters and normal point-partitions

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...

Transitive projective planes

A long-standing conjecture is that any transitive finite projective plane is Desarguesian. We make a contribution towards a proof of this conjecture by showing that a group acting transitively on the points of a non-Desarguesian projective plane must not contain any components. 1 Background definitions and main results We say that a projective plane is transitive (respectively primitive) if it ...

Transitive hyperovals in finite projective planes