Finite linear spaces with flag-transitive groups
Journal of Combinatorial Theory Series A
2-Transitive and flag-transitive designs
Proceedings of the Marshall Hall conference on Coding theory, design theory, group theory
Finite geometries
The classification of finite linear spaces with flag-transitive automorphism groups of affine type
Journal of Combinatorial Theory Series A
Classification of flag-transitive Steiner quadruple systems
Journal of Combinatorial Theory Series A
On finite linear spaces with almost simple flag-transitive automorphism groups
Journal of Combinatorial Theory Series A
A census of highly symmetric combinatorial designs
Journal of Algebraic Combinatorics: An International Journal
Mathematical Methods in Computer Science
Note: On the Cameron--Praeger conjecture
Journal of Combinatorial Theory Series A
Combinatorial Designs for Authentication and Secrecy Codes
Foundations and Trends in Communications and Information Theory
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Among the properties of homogeneity of incidence structures flag-transitivity obviously is a particularly important and natural one. Consequently, in the last decades flag-transitive Steinert-designs (i.e. flag-transitive t-(v,k,1) designs) have been investigated, whereas only by the use of the classification of the finite simple groups has it been possible in recent years to essentially characterize all flag-transitive Steiner 2-designs. However, despite the finite simple group classification, for Steiner t-designs with parameters t 2 such characterizations have remained challenging open problems for about 40 years (cf. [11, p. 147] and [12 p. 273], but presumably dating back to around 1965). The object of the present paper is to give a complete classification of all flag-transitive Steiner 4-designs. Our result relies on the classification of the finite doubly transitive permutation groups and is a continuation of the author's work [20, 21] on the classification of all flag-transitive Steiner 3-designs.