Abstract
A 2 - (υ, k, 1) design D = (ℙ,ℙ, ℬ) is a system consisting of a finite set ℙ of υ points and a collection ℬ of ℙ-subsets of ℙ, called blocks, such that each 2-subset of ℙ is contained in precisely one block. Let G be an automorphism group of a 2-(υ, k, 1) design. Delandtsheer proved that if G is block-primitive and D is not a projective plane, then G is almost simple, that is, T ⩽ G ⩽ Aut(T), where T is a non-abelian simple group. In this paper, we prove that T is not isomorphic to 3 D 4(q). This paper is part of a project to classify groups and designs where the group acts primitively on the blocks of the design.
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Liu, W. Steinberg triality groups acting on 2 ? (v, k, 1) designs. Sci. China Ser. A-Math. 46, 872–883 (2003). https://doi.org/10.1360/02ys0180
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DOI: https://doi.org/10.1360/02ys0180