2-(V,k, 1) designs admitting automorphism groups with socle 2f±(q)

Abstract

It is a large and demanding project for determining pairs (V, G) in which V is a 2-(v, k, 1) design and G is a block-transitive group of automorphisms of T>. Eighteen years ago the problem was essentially reduced to the case in which G is an almost simple group, that is, a group such that for some non-abelian finite simple group T we have T <G < Aut(T) by Camina and Praeger el at. This paper continues the works of Camina and Praeger el at. Let G act as a point-primitive block-transitive automorphism group of 2-(v, k, 1) designs V with a Ree group QFi(q) socle, we prove that the parameter k > where q = 2° for a integer a = 2n + l,n> 0. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.