On generalized hexagons of order $(3,t)$ and $(4,t)$ containing a subhexagon

Abstract

We prove that there are no semi-finite generalized hexagons with $q+1$ points on each line containing the known generalized hexagons of order $q$ as full subgeometries when $q$ is equal to $3$ or $4$, thus contributing to the existence problem of semi-finite generalized polygons posed by Tits. The case when $q$ is equal to $2$ was treated by us in an earlier work, for which we give an alternate proof. For the split Cayley hexagon of order $4$ we obtain the stronger result that it cannot be contained as a proper full subgeometry in any generalized hexagon.

13 pages, minor revisions based on referee reports, to appear in European Journal of Combinatorics

References in corpus (1)

• Some non-existence results for distance-$j$ ovoids in small generalized polygons

Cited by in corpus (1)

• Some non-existence results for distance-$j$ ovoids in small generalized polygons