MMN-1473
Nonexistence of $2-(v, k, 1)$ designs admitting automorphism groups with socle $E_8(q)$
Abstract
One of the outstanding problems in combinatorial design theory is concerning the existence of $2-(v, k, 1)$ designs. In particular, the existence of $2-(v, k, 1)$ designs admitting an interesting group of automorphisms is of great interest.
Thirty years ago, a six-person team classified $2-(v, k, 1)$ designs which have flag-transitive automorphism groups.
Since then the effort has been to classify those $2-(v, k, 1)$ designs which are block-transitive but not flag-transitive.
This paper is a contribution to this program and we prove there is nonexistence of $2-(v, k, 1)$ designs admitting a block-transitive and point-primitive but not flag-transitive automorphism group $G$ with socle $E_8(q)$.
Vol. 16 (2015), No. 2, pp. 995-1002
DOI: 10.18514/MMN.2015.1473